Function whose implementation is difficult (computationaly) to work out
If the function $f$ is computable, then $\mathrm{verify}f$ is computable too: to work out if $y=f(x)$ for some given $x$ and&nbsp;$y$, just compute $f(x)$ and see if it's equal to&nbsp;$y$. That tells you nothing about the implementation of $f$.

The relationship between the difficulty of computing $f$ and $\mathrm{verify}f$ is the essence of the P-vs-NP problem.