Inverse functions are important when we work with combining functions, especially when we add or subtract them. Here’s a simpler look at their role:

1. Understanding Function Composition: When we add or subtract functions, inverse functions help us see how the input and output are connected. For two functions, $f(x)$ and $g(x)$, if they are inverses, then using one after the other gives us back the starting input. This means if you do $f(g(x))$, you’ll end up with $x$, and if you do $g(f(x))$, you will also get $x$.

2. Real-World Applications: In everyday life, inverse functions help us understand situations where we need to go back or reverse a process. For example, if $f$ tells us how far we traveled over time, then $f^{-1}$ can help us figure out how long it took based on the distance.

3. Breaking Down Functions: In cases where we have $h(x) = f(x) + g(x)$ or $h(x) = f(x) - g(x)$, knowing the inverse functions helps us look at the possible results. For example, if $h(x) = c$, we can use $f^{-1}(c - g(x))$ to find specific results.

4. Graphing Functions: When we graph functions and their inverses, we can see how adding or subtracting changes the function. The places where the graphs cross can show important solutions related to the combined function and the inverses.

In summary, inverse functions not only help us solve equations but also make it easier to understand how different functions relate when we add or subtract them.