Question

Using ƒ(x) = 3x − 3 and g(x) = -x, find g(ƒ(x)) a. 3x+3 b. 3-3x c.-3-3x d. 2x-3

Answer 1

Answer:  Choice B.  3 - 3x

Work Shown:

$g(x) = -x\\\\g(f(x)) = -f(x)\\\\g(f(x)) = -(3x-3)\\\\g(f(x)) = -3x+3\\\\g(f(x)) = \boldsymbol{3-3x}$

Explanation: We start with the outer function g(x). In the second step, we replace every copy of x with f(x). From there we plug in f(x) = 3x-3 and simplify using the distribution rule.

The notation $g(f(x))$ is the same as writing $(g \circ f)(x)$