Remember that a function is a set of arithmetic operations being applied to an input to make an output. So the function f(x)=2x-4 multiplies an input by 2 and then subtracts 4.

There are two ways that we can find the inverse of a function. One is by working backwards from the last operation and inverting each of the operations. We will demonstrate this in the below example:

Example

Another, generally quicker, method is to follow a special algorithm. We switch the variables of the equation and then make the other variable into the subject of the equation. We will demonstrate this below in “example 12”

Exercise

Let’s complete exercise 14J on pages 233 and 234 of the textbook:

The answers are below: (N.B. 6c answer is wrong – what should it be?)