Question

F(x)=x^2+1 what is f(f(x))?

Answer 1

`f[f(x)]=x^4+2x^2+2`

Explanation:

Given function:

`f(x)=x^2+1`

To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):

`\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}`

Answer 2

f(f(x)) =
`x^(4)` + 2x² + 2

Explanation:

to evaluate f(f(x)), substitute x = f(x) into f(x)

f(f(x))

= f(x² + 1)

= (x² + 1)² + 1 ← expand factor using FOIL

=
`x^(4)` + 2x² + 1 + 1

=
`x^(4)` + 2x² + 2