To find the inverse function $g^{-1}(x)$ for the given function $g(x) = x - 2$, follow these steps:

1. Start with the equation: $y = g(x) = x - 2$ Replace $g(x)$ with $y$.

2. Solve for $x$ in terms of $y$: $y = x - 2$ Add 2 to both sides: $x = y + 2$

3. Replace $y$ with $x$ to get the inverse function: $g^{-1}(x) = x + 2$

Thus, the inverse function is $g^{-1}(x) = x + 2$.

Would you like further clarification on any of the steps?

Here are 5 related questions you can explore:

1. How do you verify if a function and its inverse are correct?
2. What are the general steps to find the inverse of a linear function?
3. How does shifting a function horizontally affect its inverse?
4. Can all functions have an inverse? If not, why?
5. What is the significance of the line $y = x$ in the context of inverse functions?

Tip: When finding an inverse function, you are essentially reversing the operations applied to the input.