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.

Learn how to find the inverse of the quadratic function y = x^2 - 4. This guide covers important algebraic concepts, including inverse functions, solving for y, and domain restrictions. Suitable for students in Grades 9-11.

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