How to find a function $f(x)$ such that $\lim_{x\to\infty}i\sqrt{1-x^2}f(x)=-1$ by maintaining the $x$ dependence?

Question

As the question itself asks, how can I find a function $f(x)$ such that $\lim_{x\to\infty}i\sqrt{1-x^2}f(x)=-1$ by maintaining the $x$ dipendence. Is there a method or is it different case by case?

I've no idea where to start and have not found anything online which I could comprehend. I'm new to this stuff so I excuse myself if the question is silly.

Thank you for your time.

EDIT:

Thanks to @qbert for his answer, he said that there are many functions that I could choose, which is the method to find them?

Answer 1

By inspection, $$ f(x)=\frac{i}{\sqrt{1-x^2}} $$ does the job.

The way I found it was by looking for a function which makes the limit trivial by cancelling any $x$ dependence (while giving a product of $-1$), making my life easier.