Question

Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following: h (h(x)) and. g (h (x))

Answer 1

H(h(x)) means to use the entire function h(x) as the x value in the function h(x)..

h(h(x)) = (x²+1)² + 1
= (x²+1)(x²+1) + 1
= (x^4 + x² + x² + 1) + 1 
= x^4 + 2x² + 2

g(h(x)) means to use the entire function h(x) as the x value in the function g(x)..

g(h(x)) = 3(x² + 1)
= 3x² + 3
g(h(x))