How to Find the Inverse Function

To find the inverse function, follow these four steps:

  1. Write the equation as a linear equation (swap f(x) with y).
  2. Swap variables x and y.
  3. Solve for y.
  4. Apply the inverse notation (replace y with f^(-1)(x)).

Example

Find the inverse function of

Solution. Let’s apply the above steps.

  1. Write the equation as a linear equation.

2. Swap variables x and y.

3. Solve for y.

Subtract 4 from both sides:

Divide both sides by 2:

You can simplify the left-hand side by separately dividing both values of the numerator:

4. Apply the inverse notation:

And there is your solution.

If you want, you can use a tool like WolframAlpha to plot your functions:

The function and the inverse are each other’s mirror images along the x = y line.

--

--

--

I’m a tech expert, entrepreneur, and software engineer from Finland. I write about programming, tech, and science. Visit my blog at www.codingem.com.

Love podcasts or audiobooks? Learn on the go with our new app.

Recommended from Medium

Solving the problem of induction

A Simple Mathematical problem that is unsolved

Maths Hack: Easily Compute the Power of a Matrix using Diagonalization

Simple Stats (Pt.4)

American mathematics contest 8

Confidence Interval and Sample Size

The Fano Plane — Hloni Introduction

A Practical Math Problem

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Artturi Jalli

Artturi Jalli

I’m a tech expert, entrepreneur, and software engineer from Finland. I write about programming, tech, and science. Visit my blog at www.codingem.com.

More from Medium

How Far Is the Horizon

Rotating a graph around the y-axis - How would we see it on an x-y plane?

A Rebel or Forced to Rebel?

A New Way Of Base Conversion: Part 5.