Can anyone come up with an explicit example of two functions $f$ and $g$ such that: $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective?
I tried the following: $f:\mathbb{R}\rightarrow \mathbb{R^{+}} $ $f(x)=x^{2}$
and $g:\mathbb{R^{+}}\rightarrow \mathbb{R}$ $g(x)=\sqrt{x}$
$f$ is not injective, and $g$ is not surjective, but $f\circ g$ is bijective
Any other examples?