An inverse function reverses the mapping of the original function.

Finding the inverse of a function

Maths

Checking and securing understanding of functions

Defining function notation

Writing composite functions

Solving equations involving functions

Solving equations involving composite functions

General algebraic forms for specific number properties

Making conjectures about patterns and relationships

Proving or disproving a statement

Writing a generalised statement about specific number properties

Writing a proof

Logical arguments

Multiple approaches to logical arguments

Problem solving with functions and proof

In this future unit, pupils continue to explore composite functions, thereby building on their work from this unit. Pupils need to understand function notation from this unit as this is used in iteration.

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In this unit pupils will further develop their understanding of algebraic notation and graphs by learning about functions, their inverses and composite functions.

Functions and proof

$${\text{f}}(x)$$ is shorthand notation for a function of $$x$$. $${\text{f}}^{-1}(x)$$ is shorthand notation for its ...

If $${\text{f}}(x)=8x+2$$ what was the value of $$x$$ that mapped to $$34$$?

Which of the below is the inverse function of $${\text{f}}(x)=7x$$?

If $${\text{f}}(17)=391$$ then $${\text{f}}^{-1}(391)=$${{}}.

A function and its inverse are a reflection of one another in the line...

If the vertical axis is labelled 'Range', what is the missing word on the horizontal axis?

For the linear equation $$y=7(x-12)$$ what is the value of the $$y$$ coordinate if $$x=6$$?

For the linear equation $$y=7(x-12)$$ what is the value of the $$x$$ coordinate if $$y=35$$?

Which of the below makes $$a$$ the subject of the equation $$7a+3=b$$?

Which of the below makes $$a$$ the subject of the equation $${1\over2}(5a-7)=b$$?

Finding the inverse of a function

Lesson outcome