I assume you're assuming $f$ is analytic, i.e. can be defined by a convergent Taylor series, otherwise it's easy to come up with counterexamples. Furthermore, I assume you're assuming $f$ is invertible, e.g. the $\sin$ function is analytic but clearly many values map to $0$. Alternatively, you'd probably need to spell out what you mean for the multiple complex roots to "approach" the multiple inverses. Indeed, even in the invertible case, you'd be comparing an increasingly large set of complex roots to the target number. I suspect the result would be unchanged between various "reasonable" choices for what it means for the set of roots to "approach" a number, but it is another area where the problem is underspecified.