The inverse of a function is found by switching the roles of $x$ and $y$, then solving for $y$. Here's how to find the inverse of $y = x^2 - 4$:

1. Start with the equation: $y = x^2 - 4$
2. Swap $x$ and $y$: $x = y^2 - 4$
3. Solve for $y$: $x + 4 = y^2$ $y = \pm \sqrt{x + 4}$

Thus, the inverse function is: $y = \pm \sqrt{x + 4}$

Since the original function $y = x^2 - 4$ is not one-to-one (it’s a parabola), its inverse isn't a function unless we restrict the domain. By restricting the domain to $x \geq 0$, we take the positive root: $y = \sqrt{x + 4}$

If you'd like further details or have any questions, let me know!

Here are 5 related questions for further exploration:

1. How do you find the inverse of a cubic function?
2. What is the domain and range of the inverse function?
3. Can all quadratic functions have inverses?
4. How does restricting the domain of a function affect its inverse?
5. How can you graphically interpret the inverse of a function?

Tip: Always check if a function is one-to-one before finding its inverse by using the Horizontal Line Test.