Question

For f(x) =3X-6
and g(x)=x+6/3
a. (fog)(x); b. (gof)(x); c. (fog)(5); d. (gof)(5)

Answer 1

a. (fog)(x) = x

b. (gof)(x) = x

c. (fog)(5) = 5

d. (gof)(5) = 5

Explanation:

These are called composite functions.

(fog)(x) can be rewritten as (f(g(x)), indicating that you will plug g(x) is as the x for f(x).

a. (fog)(x) = 3((x+6)/3)-6 = x

b. (gof)(x) = ((3x-6)+6)/3 = x

In a and b, we established that the input, x, will equal the output. We can then assume the same for c and d.

c. (fog)(5) = 3((5+6)/3)-6 = 5

d. (gof)(5) = ((3(5)-6)+6)/3 = 5