How to find f(x) - PSAT Math
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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 ?
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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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Given the functions f(x) = 2_x_ + 4 and g(x) = 3_x_ – 6, what is f(g(x)) when x = 6?
Given the functions f(x) = 2_x_ + 4 and g(x) = 3_x_ – 6, what is f(g(x)) when x = 6?
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We need to work from the inside to the outside, so g(6) = 3(6) – 6 = 12.
Then f(g(6)) = 2(12) + 4 = 28.
We need to work from the inside to the outside, so g(6) = 3(6) – 6 = 12.
Then f(g(6)) = 2(12) + 4 = 28.
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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?
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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?
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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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A function f(x) = –1 for all values of x. Another function g(x) = 3_x_ for all values of x. What is g(f(x)) when x = 4?
A function f(x) = –1 for all values of x. Another function g(x) = 3_x_ for all values of x. What is g(f(x)) when x = 4?
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We work from the inside out, so we start with the function f(x). f(4) = –1. Then we plug that value into g(x), so g(f(x)) = 3 * (–1) = –3.
We work from the inside out, so we start with the function f(x). f(4) = –1. Then we plug that value into g(x), so g(f(x)) = 3 * (–1) = –3.
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If f(x) = x² – 2 and g(x) = 3x + 5, what is f(g(x))?
If f(x) = x² – 2 and g(x) = 3x + 5, what is f(g(x))?
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To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.
Simplify: (3x + 5)(3x + 5) – 2
Use FOIL: 9x² + 30x + 25 – 2 = 9x² + 30x + 23
To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.
Simplify: (3x + 5)(3x + 5) – 2
Use FOIL: 9x² + 30x + 25 – 2 = 9x² + 30x + 23
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If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
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With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.
With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.
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What is f(–3) if f(x) = _x_2 + 5?
What is f(–3) if f(x) = _x_2 + 5?
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f(–3) = (–3)2 + 5 = 9 + 5 = 14
f(–3) = (–3)2 + 5 = 9 + 5 = 14
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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 ?
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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 =
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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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The cost of a cell phone plan is $40 for the first 100 minutes of calls, and then 5 cents for each minute after. If the variable x is equal to the number of minutes used for calls in a month on that cell phone plan, what is the equation f(x) for the cost, in dollars, of the cell phone plan for calls during that month?
The cost of a cell phone plan is $40 for the first 100 minutes of calls, and then 5 cents for each minute after. If the variable x is equal to the number of minutes used for calls in a month on that cell phone plan, what is the equation f(x) for the cost, in dollars, of the cell phone plan for calls during that month?
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40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).
40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).
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f(x) = 4x + 2
g(x) = 3x - 1
The two equations above define the functions f(x) = g(x). If f(d) = 2g(d) for some value of d, then what is the value of d?
f(x) = 4x + 2
g(x) = 3x - 1
The two equations above define the functions f(x) = g(x). If f(d) = 2g(d) for some value of d, then what is the value of d?
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f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10
f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10
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The function f, where f(x) = x2 + 6x + 8, is related to function g, where g(x) = 5 f(x-2). What is g(3)?
The function f, where f(x) = x2 + 6x + 8, is related to function g, where g(x) = 5 f(x-2). What is g(3)?
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Doing things in an orderly way is a friend to the test-taker.
g(3) = 5 f(3-2)
= 5 f(1)
= 5 \[ 12 + 6**∙**1 + 8\]
= 5 \[ 1 + 6 + 8\]
= 5 \[ 15\]
= 75
Doing things in an orderly way is a friend to the test-taker.
g(3) = 5 f(3-2)
= 5 f(1)
= 5 \[ 12 + 6**∙**1 + 8\]
= 5 \[ 1 + 6 + 8\]
= 5 \[ 15\]
= 75
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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?
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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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If f(x) = _x_2 – 5 for all values x and f(a) = 4, what is one possible value of a?
If f(x) = _x_2 – 5 for all values x and f(a) = 4, what is one possible value of a?
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Using the defined function, f(a) will produce the same result when substituted for x:
f(a) = _a_2 – 5
Setting this equal to 4, you can solve for a:
_a_2 – 5 = 4
_a_2 = 9
a = –3 or 3
Using the defined function, f(a) will produce the same result when substituted for x:
f(a) = _a_2 – 5
Setting this equal to 4, you can solve for a:
_a_2 – 5 = 4
_a_2 = 9
a = –3 or 3
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If the function g is defined by g(x) = 4_x_ + 5, then 2_g_(x) – 3 =
If the function g is defined by g(x) = 4_x_ + 5, then 2_g_(x) – 3 =
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The function g(x) is equal to 4_x_ + 5, and the notation 2_g_(x) asks us to multiply the entire function by 2. 2(4_x_ + 5) = 8_x_ + 10. We then subtract 3, the second part of the new equation, to get 8_x_ + 7.
The function g(x) is equal to 4_x_ + 5, and the notation 2_g_(x) asks us to multiply the entire function by 2. 2(4_x_ + 5) = 8_x_ + 10. We then subtract 3, the second part of the new equation, to get 8_x_ + 7.
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If f(x) = x_2 + 5_x and g(x) = 2, what is f(g(4))?
If f(x) = x_2 + 5_x and g(x) = 2, what is f(g(4))?
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First you must find what g(4) is. The definition of g(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 into f(x), we get 22 + 5(2) = 14.
First you must find what g(4) is. The definition of g(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 into f(x), we get 22 + 5(2) = 14.
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f(a) = 1/3(a_3 + 5_a – 15)
Find a = 3.
f(a) = 1/3(a_3 + 5_a – 15)
Find a = 3.
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Substitute 3 for all a.
(1/3) * (33 + 5(3) – 15)
(1/3) * (27 + 15 – 15)
(1/3) * (27) = 9
Substitute 3 for all a.
(1/3) * (33 + 5(3) – 15)
(1/3) * (27 + 15 – 15)
(1/3) * (27) = 9
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Evaluate f(g(6)) given that f(x) = _x_2 – 6 and g(x) = –(1/2)x – 5
Evaluate f(g(6)) given that f(x) = _x_2 – 6 and g(x) = –(1/2)x – 5
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Begin by solving g(6) first.
g(6) = –(1/2)(6) – 5
g(6) = –3 – 5
g(6) = –8
We substitute f(–8)
f(–8) = (–8)2 – 6
f(–8) = 64 – 6
f(–8) = 58
Begin by solving g(6) first.
g(6) = –(1/2)(6) – 5
g(6) = –3 – 5
g(6) = –8
We substitute f(–8)
f(–8) = (–8)2 – 6
f(–8) = 64 – 6
f(–8) = 58
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If f(x) = |(_x_2 – 175)|, what is the value of f(–10) ?
If f(x) = |(_x_2 – 175)|, what is the value of f(–10) ?
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If x = –10, then (_x_2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.
|–75| = 75
If x = –10, then (_x_2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.
|–75| = 75
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