The inverse of a function

If you are not sure what an inverse function is or how to find one then this video should hopefully show you.


In this tutorial you will be shown how to find the inverse of the following:

  1. \text{If}\hphantom{aa}f(x) = \dfrac{{3x - 2}}{8},\hphantom{aa}\text{find}\hphantom{aa}f^{ - 1}(x)

Inverse Example on Handling more than 1 ‘x’ term.

In this example the aim is to have two x values in the function and show that you can use other letters other than f(x)


  1. \text{If } g(x) = \dfrac{2x-3}{x-1}, x \in \mathbb{R}, x \not= 1, \text{ Find }g^{ -1}(x),

Inverse Example involving Exponential Functions

In the next example you are given an exponential function and introduced to using other notation.


  1. \text{If } h:x \to e^{(2x + 1)} \text{ find } h^{ - 1}

Inverse Examples using Natural Logs

In this example you are given a function using natural logs and asked to find the inverse.


  1. \text{If } f(x) = 2 \ln (3x - 1) \text{, } x > {\textstyle{1 \over 3}} \text{. Find } f^{ - 1}(x).