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Composite Functions (OCR GCSE Maths)

Revision Note

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Updated on

OCR Maths: HigherAQA Maths: HigherEdexcel Maths: Higher

Composite Functions

What is a composite function?

  • A composite function is a function applied to the output of another function

    • The input goes through the 1st function to become an output

    • This output goes through the 2nd function to become a new output

Worked Example

Two functions, A and B, are given by:

Function space straight A colon space space space space space space space space space input space rightwards arrow space box enclose space cross times 3 space end enclose space rightwards arrow space box enclose space minus 8 space end enclose space rightwards arrow space output space Function space straight B colon space space space space space space space space space input space rightwards arrow space box enclose space plus 5 space end enclose space rightwards arrow space box enclose space cross times 2 space end enclose space rightwards arrow space output

A composite function, C, is given by

Function space straight C colon space space space space space space space space input space rightwards arrow space box enclose Function space straight A end enclose space rightwards arrow space box enclose space Function space straight B space end enclose space rightwards arrow space output
 

(a) If the input to function C is 7, find the output.
 

Substitute the number 7 into function A

7 × 3 - 8 

Work out this value

13

Substitute 13 into function B

(13 + 5) × 2 

Work out this value

36

the output of function C is 36

(b) If the input to function C is x and the ouput is 4x, find the value of x.
 

Substitute the letter x into function A

x × 3 - 8 

Simplify this expression

3x - 8 

Substitute 3x - 8 into function B

(3x - 8 + 5) × 2 

Simplify this expression

(3x - 3) × 2
= 6x - 6 

The output is 6x - 6
The question says the output of function C is meant to be 4x
Set these two outputs equal to each other

6x - 6 = 4x 

Solve this equation to find x

2x = 6
 x = 3

x = 3

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    Author
    Reviewer
    Mark Curtis

    Author: Mark Curtis

    Expertise: Maths

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.