how to prove function is not invertible

Question

If I have a function like $f(x) = x^2$ or $f(x) = sin(x)$ in the domain $[-infty infty]$, how can I prove that they are not invertible. I guess that this would involve proving that the function is bijective, but I get lost when I actually try to do that.
How can I prove that the functions above are not invertible?

José Carlos Santos · Answer

None of the functions is injective (the first one maps $1$ and $-1$ to $1$, whereas the second one maps $=$ and $pi$ to $0$), and therefore none of them is invertible.

how to prove function is not invertible

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