What is the inverse of a function and how do you find it?

An inverse of a function is a function that does the opposite from what the original function does.

Examples:

y = x-3 [function]

x = y+3 [inverse function]

y = x³ [function]

x = 3rd root of y [inverse function]

So basically initially you express y as a function of x, and then you can rearrange it to express x in the form of y. That's how you get the inverse function.

Beware: not all functions have proper inverse functions. Some have only partial inverse functions, such as y = x².

An inverse function is the reflection of the function in the line y=x. You are swapping the constraints on the x and y values. To do this you need to rearrange the function to get y = after swapping y for x.

Original: y=2x+1

x=2y+1

x=1=2y

y=(x-1)/2, this is your inverse function.

An inverse function is undoing the operations that have been carried out in it.

So, for each operation you do the opposite to reverse it.

For example If we have a function

In order to get to y we are doing something to x.

To get the inverse we need to get back to x from y. To do this we do the opposite operations in the opposite order.

We can show this in a function machine. First we show the function by working out what operations happens to x (remembering BIDMAS/BODMAS)

Then we look at what happens to y to get back to x (each operation is the opposite and in the opposite order)

Therefor the inverse is

Checking - work out the function with the value and then test the inverse to get back to the original number.

Then work out the inverse.

The inverse takes us back to the original value