Question

Given the functions f(x) = 3x and g(x) = x² + 1, find [(gºf)(x)]- [(fºg)(x)].

Answer 1

Answer:

6x^2 - 2

Step-by-step explanation:

plug in f(x) into the g(x) formula given

g(f(x)) = (3x)^2 + 1

simplify

= 9x^2+2

plug in g(x) into the f(x) formula given

f(g(x)) = 3(x^2+1)

distribute

= 3x^2 +3

set g(f(x)) - f(g(x))

(9x^2+2) - (3x^2+3)

carry the negative

9x^2+2-3x^2-3

simplify by combining like terms

6x^2-2