Let f(x) = 3x + 2 and g(x) = −x 2 . Find f(g(−3)).

Question

Let f(x) = 3x + 2 and g(x) = −x

2

. Find f(g(−3)).

Answer 1

Hi Bijon,

This is an example of a composite function problem, where the composite function is f(g(x)) evaluated at x = -3.

All this means is that we first find out what g(-3) is (as an output value) and then take this output value and put it into the input of the function f(x).

Step by step, that looks like this:

given

f(x) = 3x + 2

g(x) = -x² (I am assuming you meant to write the 2 as an exponent)

g(-3) = -(-3)² = -9

f(g(-3)) = f(-9) = 3(-9) + 2 = -25 This is the answer

We could have also written it like this:

f(g(x)) = 3(-x²) + 2

f(g(-3)) = 3 (-(-3)²) + 2 = 3(-9) + 2 = -25