Functions (AQA GCSE Maths)

A function is a combination of one or more mathematical operations that takes a set of numbers and changes them into another set of numbers.

The notation    indicates a function , where is the input and is the output.

The input of a function is the number being put into the function, often referred to as  .

The output of a function is the number coming out of the function, often referred to as or .

To find the value of for a function , substitute into the equation of the function.

For example, if , then .

To find the value of if you know that :

• Set the equation for equal to 15

• Then solve for

For example, if and , then

A composite function is a function that 'combines' two functions.

The output of one function is used as the input for the other function.

is the notation for a composite function made up of functions and .

It means " is applied to the output of ".

I.e., first put into the function , and next put the output into the function .

Note that the function on the right () acts first, and the function on the left () acts second.

is the notation for a composite function made up of functions and .

It means " is applied to the output of ".

I.e., first put into the function , and next put the output into the function .

Note that the function on the right () acts first, and the function on the left () acts second.

To find the value of :

1. First substitute into the equation for .

2. Then substitute the output into the equation for .