IGCSE MATHEMATICS Topic : Composing Functions and Finding Inverses

Composing Functions

Some functions can be extremely complicated, for example,

It is often simpler to represent a single function as two separate functions, one carried out on the result of the first. For example, we are given the function(1)

We could define the two functionsandand then

To find we could use (1):

Or we could findthenthen

ExampleFindand

Inverses of Functions

There is a simple procedure for finding the inverse of a functionwhich is equivalent to reflecting the graph ofin the line y=x

1. Givenmake x the subject.
   
2. Swap all the x's and y's over so now there is only one y which is the subject of the equation.
   
3. Replace the single y with
   

Example:Find

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   2. 
      
   3. 
      
   Example
   
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3. 
   
4.