Confusing question about Functions

[Phrophetsam]

Let f(x) be defined as the least positive integer that can be added to x to yield a perfect
square. For example, f(5) = 4, f(9) = 7, and f(-1) = 1. Find the smallest x such that
f(x) = 99.

I haven't even begun to think of how to solve this at all. I just don't get it.

My instructor did say this

"I can accept two answers here, as long as they are explained properly. One possible answer is
a large positive integer, and another possible answer is negative."

 

[Dr.Peterson]

When I have no idea what to do, I do what children do (faced with a whole world they don't yet know about): I play with the problem to get a feel for how it works.

List maybe the integers from 1 to 20 and what f(x) is for each. Then see if there is a pattern you can recognize, and try some larger numbers to see what happens. Make hypotheses and test them. As you play, you should start discovering things.

You might want to change the experiment based on the instructor's comment! Try some negative numbers.