Let f x 8x2 5 and gx x 1 a Find the composite function

Let f (x) = 8x² + 5 and g(x) = x – 1.

(a) Find the composite function ( f o g)(x) and simplify. Show work.

(b) Find ( f o g)(2) . Show work.

Solution

f(x) = 8x² + 5

g(x) = x – 1

a) (fog)(x) = 8(x - 1)² + 5 = 8(x^2 + 1 - 2x) + 5 = 8x^2 - 16x + 13

b)  (fog)(-2) = 8(-2)^2 - 16(-2) + 13 = 77