How to find the inverse function of a one to one function?

If we truly have a one to one function then only one value for x matches one value for y, so then y has only one value for x.

We can denote an inverse of a function with
inverse function notation

Hold on how do we find the inverse of a set, it's easy all you have to do is switch all the values of x for y and all the values of y for x. Sound familiar? it comes right of the definition.

Now that we understand the inverse of a set we can understand how to find the inverse of a function.

  • Step 1: Interchange f(x) with y Interchange
  • Step 2: Interchange x and y Interchange
  • Step 3: solve for y (explicit form) and covert to inverse function notation explicit form
  • Step 4: Confirm that the function is one to one with the following check

What about functions with domain restrictions? Good question, remember if the graph is always increasing or decreasing then it's a one to one function and the domain restrictions can make that happen.

Inverse of a domain restricted function