Question

Solve the equation (f∘g)(x)=0. (Enter your answers as a comma-separated list.) f(x)=x

2
−x−2,g(x)=2x−2 x=

Answer 1

x =
`(1)/(2)` , x = 2

Explanation:

(f ￮ g)(x)

= f(g(x))

= f(2x - 2)

= (2x - 2)² - (2x - 2) - 2

= 4x² - 8x + 4 - 2x + 2 - 2

= 4x² - 10x + 4

then

(f ￮ g)(x) = 0 , that is

4x² - 10x + 4 = 0 ← divide through by 2

2x² - 5x + 2 = 0 ← in standard form

(2x - 1)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
`(1)/(2)`

x - 2 = 0 ⇒ x = 2

solutions are x =
`(1)/(2)` , 2