Question

F(x) = x² + 1
What is f(f(x))?

Answer 1

x⁴ + 2x² + 2

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

Answer 2

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

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