Can you have an input with 2 different outputs in math?

Answer 1

Yes, square root is one such example: square root of 4 is +2 or -2.

The radical symbol (√) is used to denote the positive square root of a number; ie √4 = 2;

The square root of a number is thus ±√(the number), eg square root of 4 is ±√4 = ±2.

Answer 2

Yes. This would usually be expressed as two different functions, for example, f(x) and g(x). Or you can have a single function that returns an "object" that is more complicated than a single real number - for example, a complex number (made up of two real numbers), or a point in space (3 real numbers).

Answer 3

Yes, for example, the square root of 9 is -3 or +3. One input = 9

Two outputs = -3 and +3.

But such a relationship is NOT a function.