Algebraic Functions - PSAT Math

First find the value of f(100) = 0.1(100) + 7 = 10 + 7 = 17

Then find g(17) = 1000(17) + 4 = 17000 + 4 = 17004.

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).

Plug each value for x into the above equation and solve for f(x). f(1) provides the lowest value –5/3

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.

Adding 12 to both sides and dividing by 4 yields (7y+12)/4.

By distribution we obtain **–**7x – 21 = – 7x + 20. This equation is never possibly true.

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.

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.

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

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(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

Evaluating yields –6174.

–147(–21 + 63) =

–147 * 42 = –6174

Subtract the first expression from the second. That gives you 6z = 6. That simplifies to z = 1.

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.

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.

Substitute 3 for all a.

(1/3) * (33 + 5(3) – 15)

(1/3) * (27 + 15 – 15)

(1/3) * (27) = 9

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

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

By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.