How to find f(x) - PSAT Math
Card 1 of 630
Let f(x) be defined as follows:

What is the value of 
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
. And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
. We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.

Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
, is only defined if x is less than 3 and greater than or equal to 1.

Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.

We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:

What is the value of 
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
. And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
. We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.

Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
, is only defined if x is less than 3 and greater than or equal to 1.

Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.

We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:

What is the value of 
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
. And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
. We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.

Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
, is only defined if x is less than 3 and greater than or equal to 1.

Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.

We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:

What is the value of 
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
. And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
. We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.

Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
, is only defined if x is less than 3 and greater than or equal to 1.

Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.

We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:

What is the value of 
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
. And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
. We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.

Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
, is only defined if x is less than 3 and greater than or equal to 1.

Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.

We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:

What is the value of 
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
. And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
. We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.

Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
, is only defined if x is less than 3 and greater than or equal to 1.

Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.

We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
← Didn't Know|Knew It →
Let f(x) be defined as follows:

What is the value of 
Let f(x) be defined as follows:
What is the value of
Tap to reveal answer
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as
. And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) =
. We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.

Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece,
, is only defined if x is less than 3 and greater than or equal to 1.

Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.

We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
The function f(x) is a piecewise function, which means that it is comprised of separate functions that change depending on the value of x. According to the problem, whenever x is less than 1, f(x) is defined by 2_x_ - 3. Whenever x is greater than or equal to one and less than 3, f(x) is defined as . And whenever x is greater than or equal to 3, f(x) is equal to |4_x_ – 9|.
The question asks us to find f(1) + f(3) + f(5). We need to calculate the values of f(1), f(3), and f(5) individually and then find their sum.
To find f(1), we must first decide which of the three possible functions for f(x) to use. Since f(1) means we are finding the value of f(x) when x = 1, we will have to use the second piece, which says that f(x) = . We can't use the function 2_x_ - 3, because this is only valid when x < 1, not when x = 1.
Next, we will find f(3). We need to use the third piece of the function which states that f(x) = |4_x_ – 9|. Since f(3) means we are finding f(x) when x = 3, we can only use the third piece. The second piece, , is only defined if x is less than 3 and greater than or equal to 1.
Lastly, we must find f(5). Again, we will use the function f(x) = |4_x_ – 9|, because when x = 5, x must be greater than 3.
We can now add up f(1), f(3), and f(5), which would give us 3 + 3 + 11 = 17.
The answer is 17.
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If f(x) = 5x – 10, then what is the value of 5(f(10)) – 10?
If f(x) = 5x – 10, then what is the value of 5(f(10)) – 10?
Tap to reveal answer
The first step is to find what f(10) equals, so f(10)=5(10) – 10 = 40. Then substitute 40 into the second equation: 5(40) – 10 = 200 – 10 = 190.
190 is the correct answer
The first step is to find what f(10) equals, so f(10)=5(10) – 10 = 40. Then substitute 40 into the second equation: 5(40) – 10 = 200 – 10 = 190.
190 is the correct answer
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f(x) = 0.1x + 7
g(x) = 1000x + 4
What is g(f(100))?
f(x) = 0.1x + 7
g(x) = 1000x + 4
What is g(f(100))?
Tap to reveal answer
First find the value of f(100) = 0.1(100) + 7 = 10 + 7 = 17
Then find g(17) = 1000(17) + 4 = 17000 + 4 = 17004.
First find the value of f(100) = 0.1(100) + 7 = 10 + 7 = 17
Then find g(17) = 1000(17) + 4 = 17000 + 4 = 17004.
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The rate of a gym membership costs p dollars the first month and m dollars per month every month thereafter. Which of the following represents the total cost of the gym membership for n months, if n is a positive integer?
The rate of a gym membership costs p dollars the first month and m dollars per month every month thereafter. Which of the following represents the total cost of the gym membership for n months, if n is a positive integer?
Tap to reveal answer
The one-time first-month cost is p, and the monthly cost is m, which gets multipled by every month but the first (of which there are n -1). The total cost is the first-month cost of p, plus the monthly cost for (i.e. times) n -1 months, which makes the total cost equal to p + m (n -1).
The one-time first-month cost is p, and the monthly cost is m, which gets multipled by every month but the first (of which there are n -1). The total cost is the first-month cost of p, plus the monthly cost for (i.e. times) n -1 months, which makes the total cost equal to p + m (n -1).
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- If f(x) = (x + 4)/(x – 4) for all integers except x = 4, which of the following has the lowest value?
- If f(x) = (x + 4)/(x – 4) for all integers except x = 4, which of the following has the lowest value?
Tap to reveal answer
Plug each value for x into the above equation and solve for f(x). f(1) provides the lowest value –5/3
Plug each value for x into the above equation and solve for f(x). f(1) provides the lowest value –5/3
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If n and p are positive and 100_n_3_p_-1 = 25_n_, what is n-2 in terms of p ?
If n and p are positive and 100_n_3_p_-1 = 25_n_, what is n-2 in terms of p ?
Tap to reveal answer
To solve this problem, we look for an operation to perform on both sides that will leave n-2 by itself on one side. Dividing both sides by 25_n_-3 would leave n-2 by itself on the right side of the equqation, as shown below:
100n3p–1/25n–3 = 25n/25n–3
Remember that when dividing terms with the same base, we subtract the exponents, so the equation can be written as 100n0p–1/25 = n–2
Finally, we simplify to find 4_p–_1 = _n–_2.
To solve this problem, we look for an operation to perform on both sides that will leave n-2 by itself on one side. Dividing both sides by 25_n_-3 would leave n-2 by itself on the right side of the equqation, as shown below:
100n3p–1/25n–3 = 25n/25n–3
Remember that when dividing terms with the same base, we subtract the exponents, so the equation can be written as 100n0p–1/25 = n–2
Finally, we simplify to find 4_p–_1 = _n–_2.
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If 7y = 4x - 12, then x =
If 7y = 4x - 12, then x =
Tap to reveal answer
Adding 12 to both sides and dividing by 4 yields (7y+12)/4.
Adding 12 to both sides and dividing by 4 yields (7y+12)/4.
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Which of the statements describes the solution set for **–**7(x + 3) = **–**7x + 20 ?
Which of the statements describes the solution set for **–**7(x + 3) = **–**7x + 20 ?
Tap to reveal answer
By distribution we obtain **–**7x – 21 = – 7x + 20. This equation is never possibly true.
By distribution we obtain **–**7x – 21 = – 7x + 20. This equation is never possibly true.
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If a(x) = 2x3 + x, and b(x) = –2x, what is a(b(2))?
If a(x) = 2x3 + x, and b(x) = –2x, what is a(b(2))?
Tap to reveal answer
When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–43) + (–4), which equals –132.
When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–43) + (–4), which equals –132.
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x f(x) g(x) 9 4 0 10 6 1 11 9 0 12 13 –1
According to the figure above, what is the value of g(12) – √f(9)?
| x | f(x) | g(x) |
|---|---|---|
| 9 | 4 | 0 |
| 10 | 6 | 1 |
| 11 | 9 | 0 |
| 12 | 13 | –1 |
According to the figure above, what is the value of g(12) – √f(9)?
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For this question, we "plug in" the value of x given, which is inside the parentheses, and follow along the table to see what value the f or g functions output. For g(12), the output value is –1, while for f(9), the output value is 4 (be careful not to reverse these!) Thus, we can plug into the equation given:
(–1) – √4) = –1 – 2 = –3.
For this question, we "plug in" the value of x given, which is inside the parentheses, and follow along the table to see what value the f or g functions output. For g(12), the output value is –1, while for f(9), the output value is 4 (be careful not to reverse these!) Thus, we can plug into the equation given:
(–1) – √4) = –1 – 2 = –3.
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If
and
, what is
?
If and
, what is
?
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g is a function of f, and f is a function of 3, so you must work inside out.
f(3) = 11
g(f(3)) = g(11) = 121 + 11 = 132
g is a function of f, and f is a function of 3, so you must work inside out.
f(3) = 11
g(f(3)) = g(11) = 121 + 11 = 132
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Let f(x, y) = x2y2 – xy + y. If a = f(1, 3), and b = f(–2, –1), then what is f(a, b)?
Let f(x, y) = x2y2 – xy + y. If a = f(1, 3), and b = f(–2, –1), then what is f(a, b)?
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f(x, y) is defined as x2y2 – xy + y. In order to find f(a, b), we will need to first find a and then b.
We are told that a = f(1, 3). We can use the definition of f(x, y) to determine the value of a.
a = f(1, 3) = 1232 – 1(3) + 3 = 1(9) – 3 + 3 = 9 + 0 = 9
a = 9
Similarly, we can find b by determining the value of f(–2, –1).
b = f(–2, –1) = (–2)2(–1)2 – (–2)(–1) + –1 = 4(1) – (2) – 1 = 4 – 2 – 1 = 1
b = 1
Now, we can find f(a, b), which is equal to f(9, 1).
f(a, b) = f(9, 1) = 92(12) – 9(1) + 1 = 81 – 9 + 1 = 73
f(a, b) = 73
The answer is 73.
f(x, y) is defined as x2y2 – xy + y. In order to find f(a, b), we will need to first find a and then b.
We are told that a = f(1, 3). We can use the definition of f(x, y) to determine the value of a.
a = f(1, 3) = 1232 – 1(3) + 3 = 1(9) – 3 + 3 = 9 + 0 = 9
a = 9
Similarly, we can find b by determining the value of f(–2, –1).
b = f(–2, –1) = (–2)2(–1)2 – (–2)(–1) + –1 = 4(1) – (2) – 1 = 4 – 2 – 1 = 1
b = 1
Now, we can find f(a, b), which is equal to f(9, 1).
f(a, b) = f(9, 1) = 92(12) – 9(1) + 1 = 81 – 9 + 1 = 73
f(a, b) = 73
The answer is 73.
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Let F(x) = _x_3 + 2_x_2 – 3 and G(x) = x + 5. Find F(G(x))
Let F(x) = _x_3 + 2_x_2 – 3 and G(x) = x + 5. Find F(G(x))
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F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)
F(G(x)) = (x + 5)3 + 2(x + 5)2 – 3 = x_3 + 17_x_2 + 95_x + 172
G(F(x)) = _x_3 + _x_2 + 2
F(x) – G(x) = _x_3 + 2_x_2 – x – 8
F(x) + G(x) = _x_3 + 2_x_2 + x + 2
F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)
F(G(x)) = (x + 5)3 + 2(x + 5)2 – 3 = x_3 + 17_x_2 + 95_x + 172
G(F(x)) = _x_3 + _x_2 + 2
F(x) – G(x) = _x_3 + 2_x_2 – x – 8
F(x) + G(x) = _x_3 + 2_x_2 + x + 2
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What is the value of xy_2(xy – 3_xy) given that x = –3 and y = 7?
What is the value of xy_2(xy – 3_xy) given that x = –3 and y = 7?
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Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
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