How to Find the Inverse Function

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.

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