Question

Functions f , g: R → R are defined, respectively, by f(x) = x 2 + 3x + 1, g(x) = 2x – 3, find f o f

Answer 1

Given, f(x) = x² + 3x + 1, g(x) = 2x – 3

fof = f(f(x))

= f(x² + 3x + 1)

= (x² + 3x + 1)² + 3(x² + 3x + 1) + 1

= x⁴ + 9x² + 1 + 6x³ + 6x + 2x² + 3x² + 9x + 3 + 1

= x⁴ + 6x³ + 14x² + 15x + 5