You need to be able to work with function notation confidently in your exam
Composite functions
If you apply two functions one after the other, you can write a single function which has the same effect as the two combined functions
This is called a composite function
Working it out
Order is important in composite functions
You can think of fg(x) as f(g(x))
You work out g(x) first then you use this answer as your input for f(x)
To find an algebraic expression for fg(x) you need to substitute the whole expression for g(x) for each instance of x in the expression for f(x)
Inverse functions
For a function f the inverse of f is the function that undoes f
You write the inverse of f(-1)
If you apply f then f(-1) you will end up back where you started
* If you apply f then f(-1) you have applied the composite function f(-1)f
* The output of f(-1)f is the same as the input
Finding the inverse
To find the inverse of a function given in the form f(x) you need to
* Write the function in the form y=
* Rearrange to make x the subject
* Swap any y’s for x’s and rewrite as f(-1)(x) =
Methods
You can sometimes use a flow chart to find an inverse
Here is an example flow chart for f(x)
+3, x5
You would then work backwards through the flow chart to find f(-1)(x)
/5 -3
You subtract 3 then divide by 5
* You could then write this in algebraic form