Maple Inverse Function $y=x^2-2$

Question

I have this assignment:

Consider the function $f : [0, ∞) → [−2,∞)$ defined by $f(x) = x^2 − 2$. Which statement about the inverse function $f^{−1}$ is true (the inverse)?

I am having a hard time finding out how to do this. The function f(x)=x^2-2 itself cannot be invertible, as it is not one-to-one. But with the specified domain and codomain, it is invertible. How can you specify these in Maple?

The answer is:

$f^{−1}(x) = \sqrt{x + 2}$

I just do not know how to solve it.

EDIT: If you got a few choices like me (a multiple choice test), you can just try inverting each choice, and the one that inverts back to the function in the question is the right one.

Answer 1

RIGHT ANSWER: If you got a few choices like me (a multiple choice test), you can just try inverting each choice, and the one that inverts back to the function in the question is the right one.

Answer 2

The inverse satisfies

$$ f(f^{-1}(x)) = (f^{-1}(x)^2 - 2 = x $$

Solving this gives two solutions

$$ f^{-1}(x) = \pm \sqrt{x+2} $$

We want $f^{-1}: [-2,\infty) \to [0,\infty)$, so the positive square root is the correct answer

The other possibility is $f: (-\infty,0] \to [-2,\infty)$ which inverts to the negative square root