Question

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

Answer 1

Answer

Find out f(f(x)) .

To prove

As given in the question

f(x) = x² + 1

Now

f(f(x)) = f (x² + 1)

Now find out the value of f (x² + 1).

f(f(x)) = f (x² + 1)

= (x² + 1)² + 1

Using formula

(a + b)² = a² + b² + 2ab

Apply in the above function

f(f(x)) = (x² + 1)² + 1

f(f(x)) =
`x^(4)` + 1 +
`2x^(2)` + 1

Simplify

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

Thus the value of f(f(x)) is: f(f(x)) =
`x^(4)` +
`2x^(2)` + 2

Explanation: