let f(x)=3x+2 and g(x)=2x^2+2x. after simplifying (f o g)(x)

Answer 1

let f(x)=3x+2 and g(x)=2x^2+2x. after simplifying (f o g)(x) = f (g(x) ) = f ( 2x^2+2x ) = 3(2x^2+2x) + 2 = 6x^2 + 6x + 2

Answer 2

This is a composite function problem where you've been given functions f(x) and g(x).

(f o g)(x) can also be written as f(g(x)) where you replace x in f(x) with the function g(x).

Since you're given f(x) = 3x +2, you replace that x with g(x) = 2x² + 2x

resulting in (f o g)(x) = f(g(x)) = 3(2x² + 2x) + 2

Note how g(x) is now in the function f(x) which multiplies x by 3 and adds 2.

Simplify by multiplying g(x) by 3 and adding 2, so (f o g)(x) = 6x² + 6x + 2