Which function has an inverse that’s also a function?

Inverse of a function is also a function, if and only if the function is One - to - One. This means no y value occurs in the range of the function more than once. 

If we observe the given options, we can see option  B, C and D have some repeated values of y. Only the function in option A is one to one. Hence the inverse of function given in option A will also be a function.

So, the answer to this question is option A