Why is this relation a function?

Question

I need to determine whether or not the relation $\{ (a^2,a) | a \in \Bbb {R}, a \geq 0\}$ is a function from $\Bbb {R}$ to $\Bbb {R}$.

I think that it is a function. But I don't know how to justify my reasoning besides saying that $a^2$ can only map to $a$. 4 Only maps to 2, 9 only maps to 3

Answer 1

Hint: Since $a^2$ gets mapped to $a$, what does $x$ get mapped to, where $x$ is any nonnegative real number? If there's a unique answer, then you have a function. Otherwise, it is not a function.