Answer:
(g ◦ h) (x) = 16x² + 12x -4
Explanation:
We have
g(x) = x² − 5x
h(x)= 4x + 4
(g ◦ h) (x) = g(h(x))
h(x) = 4x + 4
g(h(x)) = g(4x + 4)
= (4x + 4)² - 5(4x+4) //substitute 4x + 4 wherever there is an s-term in
(4x + 4)² = 16x² + 32x + 16
5(4x + 4) = 20x + 20
(4x + 4)² - 5(4x+4) = 16x² + 32x + 16 -(20x + 20)
= 16x² + 32x + 16 - 20x - 20
= 16x² +(32x - 20x) + (16-20)
= 16x² + 12x -4