What is the inverse function for f(x) = x^2?

To find the inverse function of f(x) = x², we start by replacing f(x) with y:

y = x²

Next, we swap x and y. This gives us:

x = y²

Now, we solve for y:

y = √x

However, we need to consider the domain of the original function. The function f(x) = x² is not one-to-one over all real numbers, as both positive and negative values of x produce the same output. Therefore, we define the inverse function only for x ≥ 0.

Thus, the inverse function is:

f^-1(x) = √x, for x ≥ 0.