F (x) = x² + 1

What is f (f (x)) ?

x⁴ + 2x² + 2

Step-by-step explanation:

f (x) = x² + 1

f (f (x)) = (f (x)) ² + 1

f (f (x)) = (x² + 1) ² + 1

f (f (x)) = x⁴ + 2x² + 1 + 1

f (f (x)) = x⁴ + 2x² + 2

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

Step-by-step explanation:

f (f (x)) = f (x), with the equation plugged into itself.

That means that if f (x) = x^2 + 1, then:

f (f (x)) = (x^2 + 1) ^2 + 1 - ->

f (f (x)) = x^4 + 2x^2 + 1 + 1 - ->

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