Real-world uses of combining functions and finding their inverses can make math feel more relevant! Here are two clear examples:

1. Finance: Imagine using functions to help with money matters. You can have one function for your income and another for your expenses. By putting them together, you can see how much money you have overall. You would write it like this: $B(t) = I(t) - E(t)$. Here, $B$ stands for your budget, $I$ is for your income, and $E$ is for your expenses.

2. Physics: In physics, using inverse functions helps us understand things like how fast something is moving over time. If you have a function for distance, called $d(t)$, its inverse $t(d)$ tells you how long it takes to travel that distance.

These examples show that by combining and inverting functions, we can make better choices—whether we are managing our budget or studying motion!