I came across the following problem in a prelim question paper. The question as stated seems meaningless to me, I am adding the picture so as to avoid any error from my end.
My case with the above question is that $f$ is given to be defined on $(0,1)$ so $f(x)$ makes sense only if $x\in (0,1)$. Although, it doesn’t tell s anything but if we assume therefore that the range is contained only in $(0,1)$. But then it would mean that a point $x$ is taken only $0$ times which is again a nonsense.
I am not sure if I am missing something or the question is really wrong. If it is wrong, what can be “the nearest correct” version of it? Meaning if we take the function to be defined from $\mathbb{R}$ to $(0,\infty)$?