Inverse Functions (OCR GCSE Maths)

Inverse Functions

What is an inverse function?

• An inverse function does the opposite (reverse) operation of the function it came from

  • E.g. If a function “doubles the number then adds 1”

  • Then its inverse function “subtracts 1, then halves the result”

    • The same inverse operations are used when solving an equation or rearranging a formula

• An inverse function performs the inverse operations in the reverse order

• The inverse of is 

  • The order of the boxes is reversed

  • The operation is replaced by its inverse operation

    • × ↔ ÷ and  + ↔ -

• If a number goes through a function, then that result goes through the inverse function, you get back the same number again!

How do I find an inverse function algebraically?

• If putting x into a function gives out y, then putting y into the inverse function gives back x

• Inverse functions are related to rearranging formulae

  • Let's say a function is 

    • It's inverse is therefore 

  • In algebra, the original function is

  • Look what happens when you make x the subject

    • 

    • This is the function  

    • The operations are identical to that of the inverse function! (the input here is a y though)

  • Swapping the x and y shows the inverse function more clearly

    •