Final answer:
To find the inverse of a function, follow these steps:
1. Switch the variables x and y in the original function.
2. Solve for y.
3. Interchange x and y again to get the inverse function.
Explanation:
The inverse of a function is the opposite of the original function. It takes the output of the original function as input and returns the original input. Not all functions have inverses, but if a function does have an inverse, it is unique and can be found using the steps above.
Let's take an example to illustrate this process. Consider the function f(x) = 2x + 3. To find its inverse, we follow these steps:
1. Switch x and y: y = 2x + 3
2. Solve for x: x = (y - 3) / 2
3. Interchange x and y: y = (x - 3) / 2 (this is the inverse function)
So, the inverse of f(x) is g(y) = (y - 3) / 2. We can check that this is indeed the inverse by verifying that g(f(x)) = x and f(g(y)) = y for all values of x and y. This is known as the horizontal line test, which ensures that the inverse function undoes what the original function does.