If $H(x)$ is a one-way function, is $f(x)=H(x)\cdot x^{-1}$ a one-way function? Assume $S$ is a domain. $S' \subseteq S$ and all elements in $S'$ are invertible.  $H:S'\rightarrow S$. If $H(x)$ is a one-way function, is $f(x)=H(x)\cdot x^{-1}$ a one-way function?
Let ${y=x^{-1}}$. if ${f(x)}$ is a bijective function. then we can avoid ${H(x) \cdot y= H(x) \cdot y'}$, where every ${x}$ has unique ${f(x)}$