GCSE Tutoring Programme
Our chosen students improved 1.19 of a grade on average - 0.45 more than those who didn't have the tutoring.
In order to access this I need to be confident with:
Squares and square roots Cubes and cube roots BIDMAS Rearranging equations TrigonometryThis topic is relevant for:
Here we will learn about inverse functions including what an inverse function is, the notation used for an inverse function and how to find an inverse function.
There are also inverse function worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
Inverse functions are functions which reverse or βundoβ another function.
To write the inverse of the function , we use the notation .
We have seen how to use a function machine to work backwards to find the input from a known output. If we were to write the algebraic expression relating to these inverse operations in the correct order, we would have found the inverse function.
To find an inverse function we need to rewrite the function using y as the unknown variable and set the function equal to x. Then we need to rearrange the function to make y the subject and write the function using the inverse function notation.
E.g.
Inverse functions can be used to solve equations or find missing values on graphs if we know the value.
Inverse functions are also used when finding an unknown angle in a triangle using trigonometry.
E.g.
When finding a missing angle or solving the equation , we would need to use the inverse of the sine function,
In A level mathematics instead of using and the inverse trigonometric functions have different names. We would use arcsin, arccos and arctan.
We also look at when inverse functions can exist. Functions such as quadratics, cubics, sin, cos and tan must have a restricted domain (a limit to which values are allowed).
We also look at how to find the graph of the inverse function by reflecting the graph of the function in the line .
In order to find an inverse function:
Get your free inverse functions worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEGet your free inverse functions worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEInverse functions is part of our series of lessons to support revision on functions in algebra. You may find it helpful to start with the main functions in algebra lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
If , find
2Rearrange the equation to make the subject.
3Write your inverse function using the notation.
If find .
Write out the expression for the original function using a instead of the . Set this expression equal to
Rearrange the equation to make the subject.
Write your inverse function using the notation.
Use because the original function was
If find .
Write out the expression for the original function using a instead of the . Set this expression equal to
Rearrange the equation to make the subject.
An inverse function cannot have two different outputs for one input so we only need the positive square root.
Write your inverse function using the notation.
If , find .
Write out the expression for the original function using a instead of the . Set this expression equal to
Rearrange the equation to make the subject.
Write your inverse function using the notation.
A common error is to think the inverse function will be the reciprocal of the function because of the βpower of β notation.
E.g.
If an incorrect expression for would be or .
1. If find
Rearranging the formula, first add then divide by
2. If find
Rearranging the formula, first subtract then multiply by
3. If find :
Rearranging the formula, first add to both sides, then subtract from both sides.
4. If find
Rearranging the formula, first add then cube root.
5. If find :
Rearranging the formula, first subtract then square and expand the brackets.
6. If find :
See working and use example to help.
1. (a) If find
(b) If find
(4 marks)
(a)
Attempt the rearrange formula
(1)
(1)
(b)
Attempt the rearrange formula
(1)
or
(1)
2. If and
(a) Find
(b) Find when
(6 marks)
(a)
Set or find
(1)
Answer of
(1)
(b)
(1)
Set equal
(1)
Get on one side of the equation
(1)
Answer of
(1)
3. If find
(4 marks)
Multiplying by denominator
(1)
Expand and isolate
(1)
y factored out
(1)
(1)
You have now learned how to:
Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.
Find out more about our GCSE maths tuition programme.
Notifications