Question

Let f(x) = 4x-8 and g(x)=x+3. Find f(g(x)) and g(f(x)).

f(g(x)) = (Simplify your answer.)
g(f(x)) =
(Simplify your answer.)

Answer 1

`\huge{ \bold{f(g(x)) = 4x + 4}} \\ \\ \huge{ \bold{g(f(x)) = 4x - 5}}`

Explanation:

f(x) = 4x-8

g(x)=x+3

In order to find f(g(x)) you substitute g(x) into f(x) that's where ever you find x in f(x) you replace it with g(x) and solve

We have

`f(g(x)) = 4(x + 3) - 8 \\ = 4x + 12 - 8 \\ = 4x + 4`

In order to find g(f(x)) you substitute f(x) into g(x) that's where ever you find x in g(x) you replace it with f(x) and solve

We have

`g(f(x)) = (4x -8) + 3 \\ = 4x - 8 + 3 \\ = 4x - 5`

Hope this helps you