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Inverse Functions (Edexcel A Level Maths): Revision Note

Exam code: 9MA0

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Paul

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Edexcel Maths: PureOCR Maths A: PureAQA Maths: Pure

Inverse functions

What is an inverse function?

  • An inverse function is the opposite to the original function

  • An inverse function is denoted by f to the power of negative 1 end exponent left parenthesis x right parenthesis

  • The inverse of a function only exists if the function is one-to-one

  • Inverse functions are used to solve equations

    • The solution of space f left parenthesis x right parenthesis equals 5 is x equals f to the power of negative 1 end exponent left parenthesis 5 right parenthesis

 

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

 

How do I sketch the graph of an inverse function?

Inverse Functions Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

 

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

What is the domain and range of an inverse function?

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 find an inverse function using algebra?

  • 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

  • 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

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

Author: Paul

Expertise: Maths Content Creator

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.