Inverse Functions (Cambridge (CIE) A Level Maths) : Revision Note

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Inverse Functions

Inverse functions

  • An inverse function is the opposite to the original function

  • It is denoted by f-1(x)

  • An inverse only exists for one-to-one functions

 

Inverse Functions Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

Graphs of inverse functions

  • The graphs of a function and its inverse are reflections in the line y = x

1-3-3-inverse-functions-notes-diagram-2

Domain and range of inverse functions

Inverse Functions Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

 

  • The range of a function will be the domain of its inverse function

  • The domain of a function will be the range of its inverse function 

How do I work out an inverse function?

  • Set y = f(x) and make x the subject

  • Then rewrite in function notation

  • Domain is needed to fully define a function

  • The range of f is the domain of f-1 (and vice versa)

 

Inverse Functions Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes

 

... and finally …

  • A function (f) followed by its inverse (f-1) will return the input (x)

  • ff-1(x) = f-1f(x) = x (for all values of x)

 

Inverse Functions Notes Diagram 5, A Level & AS Level Pure Maths Revision Notes

Worked Example

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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.

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