Question

Find (fog)(x) and (gof)(x).

f(x) = 5x - 3
g(x) = -x - 8

Write your answer as a polynomial in simplest form.

(fog)(x) =

(gof)(x) =

Answer 1

(fog)(x) = -5x - 43.

(gof)(x) = -5x - 5.

Step-by-step explanation:

To find (fog)(x), we substitute g(x) into f(x).

So, (fog)(x) = f(g(x)).

Substituting -x - 8 for x in f(x) = 5x - 3, we get:

(fog)(x) = 5(-x - 8) - 3.

Simplifying, (fog)(x) = -5x - 40 - 3

= -5x - 43.

To find (gof)(x), we substitute f(x) into g(x).

So, (gof)(x) = g(f(x)).

Substituting 5x - 3 for x in g(x) = -x - 8, we get :

(gof)(x) = -(5x - 3) - 8.

Simplifying, (gof)(x) = -5x + 3 - 8

= -5x - 5.