I recently read about OWFs and realized that the composition of two OWFs (called, say, $g$ and $f$) are not necessarily an OWF. However, if I modify the question a little bit and fix $g$ to be an injective function, with $f$ still being an OWF, is their composition $g(f(x))$ a one-way function?
I now understand the intuition, thanks to the comments.
If $g$ is no longer one-to-one, can we prove that the composition of $g$ and $f$ is not always a one-way function in the same way as to how we proved that $f2(x)$ is not an OWF here?
