Question

The functions f, g and h on the set of real numbers are defined by f(x) = x² + 1, g(x) = 2x - 3 and h(x) = 4x + 5 respectively. Determine the formulae for the composite functions:

(a) f [g(x)]
(b) g [h(x)]
(c) h [g {f(x)} ]​

Answer 1

f[g(x)] = (2x-3)²+1 = 4x²-12x+10
g[h(x)] = 2(4x+5)-3 = 8x+7
h[g{f(x)}] => 2(x²+1)-3 = 2x²-1
4(2x²-1)+5 = 8x²+1