Inverse of $y = x^{2}$

Find the inverse of the function $y = x^{2}$.

To find the inverse function, swap $x$ and $y$, and solve the resulting equation for $y$.

This means that the inverse is the reflection of the function over the line $y = x$.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: $y = x^{2}$ becomes $x = y^{2}$.

Now, solve the equation $x = y^{2}$ for $y$.

$y = \sqrt{x}$

$y = - \sqrt{x}$

$y = \sqrt{x}$A

$y = - \sqrt{x}$A

Graph: see the graphing calculator.