Composite Functions (Edexcel IGCSE Maths A (Modular))
Revision Note
Written by: Mark Curtis
Reviewed by: Dan Finlay
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Composite Functions
What is a composite function?
A composite function is a function applied to the output of another function
Composite functions may also referred to as compound functions
What notation is used for composite functions?
If and are two functions, then
is a composite function
Also written
It means the input goes through function first
This gives the output
Then this output, , becomes the input of function , giving
is the shorthand notation used for
It means do first, then
The order of applying the functions goes from right to left
(the letter nearest the bracket goes first)
This is often the opposite of what people expect!
means do first then second
means apply twice!
This can be written
This does not mean the same as
Examiner Tips and Tricks
A good trick in the exam is to write brackets around to make it , to see that it is "g" of "f(x)".
How do I substitute numbers into composite functions?
If you are putting a number into a composite function
put the number into the function closest to (x)
then make the output of the first function the input of the second function
For example, if and
to find :
Put the 2 in as the input of first
Then put 5 in as the input of
So
to find :
Put the 2 in as the input of first
Then put in as the input of
So
to find :
so
How do I find composite functions algebraically?
If you are using algebra, substitute the whole algebraic expression as your input
For example, if and
which simplifies to
Worked Example
In this question, and .
(a) Find .
"g" is on the inside of the composite function, so apply g first
Now apply the function "f" to 36
(b) Find .
"f" is on the inside of the composite function so substitute the function f(x) into g(x)
It can help to write
Simplify inside the bracket
You do not need to expand the answer
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