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)`