Given that f(x) = x squared + 2x and g(x) = -5x + 3, determine each of the following. Make sure to fully simplify. (Please show me step by step.)

Question

(f °g)(x)=

(g°f)(x)=

Answer 1

f(x) = x² + 2x

g(x) = -5x + 3

(g _° f)(x) = g(f(x)) = g(x² + 2x) = -5(x² + 2x) + 3 = -5x² - 10x + 3

(f _° g)(x) = f(g(x)) = f(-5x + 3) = (-5x + 3)² + 2(-5x + 3)

= (-5x + 3)(-5x + 3) + 2(-5x + 3)

= 25x² - 15x - 15x + 9 - 10x + 6

= 25x² - 40x + 15