Question

If f(x)=3x^(2)+1 and G(x)=2x-3 what would f(f(x))

Answer 1

Hello,

`(fof)(x)=f(f(x))\\\\=3(3x^2+1)^2+1\\\\=3(9x^4+6x^2+1)+1\\\\\boxed{=27x^4+18x^2+4}`

Answer 2

f(f(x)) = 27
`x^(4)` + 18x² + 4

Explanation:

To find f(f(x)) substitute x = f(x) into f(x) , that is

f(3x² + 1)

= 3(3x² + 1)² + 1 ← expand parenthesis using FOIL

= 3(9
`x^(4)` + 6x² + 1) + 1 ← distribute parenthesis by 3

= 27
`x^(4)` + 18x² + 3 + 1 ← collect like terms

= 27
`x^(4)` + 18x² + 4