Online Test Banks
Score higher
See Online Test Banks
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

How to Invert a Function to Find Its Inverse

If you’re given a function and must find its inverse, first remind yourself that domain and range swap places in the functions. Literally, you exchange f(x) and x in the original equation. When you make that change, you call the new f(x) by its true name — f–1(x) — and solve for this function.

For example, follow the steps to find the inverse of this function:

  1. Switch f(x) and x.

    When you switch f(x) and x, you get


    (Note: To make the notation less clumsy, you can rewrite f(x) as y and then switch x and y.)

  2. Change the new f(x) to its proper name — f–1(x).

    The equation then becomes

  3. Solve for the inverse.

    This step has three parts:

    1. Multiply both sides by 3 to get 3x = 2f–1(x) –1.

    2. Add 1 to both sides to get 3x + 1 = 2f–1(x).

    3. Lastly, divide both sides by 2 to get your inverse:

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus

Inside Sweepstakes

Win $500. Easy.