Composite Function

Question

Given f (x)= 4x² - x + 2 and g (x) = 2 x² -1, compute and simplify the following :

(f . g) (x)

Answer 1

Here we take g(x) and "put it inside" f(x). Anytime we see x in f(x), we replace it with g(x)

(f . g)(x) = f(g(x)) = f(2x²-1) = 4(2x²-1)² - (2x²-1) + 2

= 4(4x⁴ - 4x² + 1) - 2x² + 1 + 2

= 16x⁴ - 16x² + 4 - 2x² + 3

= 16x⁴ -18x² + 7