Question

10. Given f(x) = 3x + 7 and g(x) = 2x+5. [6 points] a. Find f(g(x)) b. Find g(f(x))

Answer 1

`\huge{ \boxed{f(g(x)) = 6x + 22}}`

`\huge{ \boxed{g(f(x)) = 6x + 19}}`

Explanation:

`f(x) = 3x + 7 \\ g(x) = 2x + 5`

a.

To find f(g(x)), substitute g(x) into f(x). That is for every x in f(x) replace it with g(x) and simplify.

`f(g(x)) = 3(2x + 5) + 7 \\ f(g(x)) = 6x + 15 + 7 \\f(g(x)) = 6x + 22 \: \: \: \: \: \: \: \: \: \:`

b.

To find g(f(x)), substitute f(x) into g(x). That is for every x in g(x) replace it with f(x) and simplify.

`g(f(x)) = 2(3x + 7) + 5 \\ = 6x + 14 + 5 \\ = 6x + 19 \: \: \: \: \: \: \: \:`