>>14254877The squaring function, f(x) = x^2, does not a true inverse as it is not injective. For example, as you've essentially highlighted, f(-2) = f(2) = 4. Sometimes we'll say then that the square root of 4 is ±2, but we're not invoking a function here since a function can provide only one output by definition. Rather, we're considering the output of two functions, the two distinct "branches" of the fiber (or preimage) of the squaring function. When we pick one, we usually go with the positive branch. This means, perhaps surprisingly, that you may find yourself saying "((-2)^2)^1/2 = 2." We also do a similar thing for the complex logarithm, but that has an infinite number of branches for us to choose from; this is a completely arbitrary decision.
