To find the inverse of a combined function, you can follow these easy steps. Let’s break it down:

1. Know Your Combined Function: First, figure out if you’re adding, subtracting, multiplying, or dividing two functions, like ( f(x) ) and ( g(x) ).

2. Find Each Function's Inverse: Next, you need to find the inverses for both functions, which we can call ( f^{-1}(x) ) and ( g^{-1}(x) ).

3. Do the Operations the Right Way:

   • Addition: If you have ( h(x) = f(x) + g(x) ), then the inverse will be ( h^{-1}(x) = f^{-1}(x) + g^{-1}(x) ).
   • Subtraction: For ( h(x) = f(x) - g(x) ), the inverse becomes ( h^{-1}(x) = f^{-1}(x) - g^{-1}(x) ).
   • Multiplication: If ( h(x) = f(x) \cdot g(x) ), then the inverse is found by using ( h^{-1}(x) = \frac{f^{-1}(x)}{g^{-1}(x)} ).
   • Division: For ( h(x) = \frac{f(x)}{g(x)} ), the inverse is ( h^{-1}(x) = g^{-1}(x) / f^{-1}(x) ).

4. Rearrange the Equations: Finally, if you need to, rearrange the equations so they look more like ( y ) and ( x ). This makes it clearer.

That’s about it! Just keep in mind, finding the inverse might take a little bit of extra work. Happy mathing!