Question

Given f(x)=-5x+2, and g(x) = 4x²-3x-6, find f(g(2)).

A. 12
B. 22
C. 52
D. 72

Answer 1

To find f(g(2)), first evaluate g(2) which is 4, then substitute this value into f(x) to get f(4) which is -18.

Step-by-step explanation:

The question involves composition of functions, specifically finding the value of f(g(2)). This requires two steps:

1. Evaluate g(2) by substituting x with 2 in the function g(x).
2. Substitute the result from step 1 into the function f(x) and solve to find f(g(2)).

Applying these steps:

1. g(2) = 4(2)² - 3(2) - 6 = 16 - 6 - 6 = 4

2. f(g(2)) = f(4) = -5(4) + 2 = -20 + 2 = -18

Therefore, the value of f(g(2)) is -18.