How do you find the inverse of a function?

So you are asked to find the inverse of a function f(x).
The inverse function is denoted by f -1(x).
To help with this we can use the identity f(f -1(x))=x.
Now, we need to define y=f -1(x).
x=f(f -1(x))=f(y)=2y+1                    As f(y) is similar to f(x) but with the variable change of x to y
Hence, we need to solve:           
x-1=2y                                                  Minus 1 from each side of the equation
½(x-1)=y=f -1(x)                                                As we defined f -1(x)=y
Therefore, we have found the inverse function: f -1(x) = ½(x-1)

We can continue further and find the domain and range of an inverse function using the identities:
Domain f(x) = Range f -1(x)
Range f(x) = Domain f -1(x)

Ryan J. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

1 year ago

Answered by Ryan, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Andrew B. A Level Economics tutor, GCSE Economics tutor, 13 Plus  Mat...
View profile
£20 /hr

Andrew B.

Degree: Economics L100 (Bachelors) - Exeter University

Subjects offered: Maths, Economics


“About Me: I am an economics student at Exeter University, I have a real passion for economics and how applicable it is to the world around us, and I hope my enthusiasm for it comes across in my tutorials and helps to inspire you! I'm...”

Andrew D. A Level Maths tutor, GCSE Maths tutor, A Level Further Math...
View profile
£20 /hr

Andrew D.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“About me Hi, I'm Andrew. I'm currently going into my second year studying maths at the University of Warwick. I find maths incredibly fascinating, as my passion stems from the idea thatmaths is everywhere and is fundamental to underst...”

MyTutor guarantee

Fahad M. A Level Maths tutor, A Level Chemistry tutor, A Level Biolog...
View profile
£30 /hr

Fahad M.

Degree: Medicine And Surgery - MBChB (Bachelors) - Birmingham University

Subjects offered: Maths, Psychology+ 7 more

.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“About MeGraduating highschool with many distinctions I went on to become a medical student at the University of Birmingham. Having excelled in my interview (gaining the top rank in Motivation and Experience) I went on immediately to ...”

About the author

Ryan J. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...
View profile

Ryan J.

Currently unavailable: for new students

Degree: Mathematics (Bachelors) - Durham University

Subjects offered: Maths, Further Mathematics + 1 more

Further Mathematics

“Hi, I’m Ryan, a second year mathematician at Durham University and I have a drive and passion to become a tutor in mathematics. I have two years of experience tutoring a group of AS level maths students so I feel I have the understand...”

MyTutor guarantee

You may also like...

Posts by Ryan

How do you find the inverse of a function?

How to integrate lnx by parts?

What are the differences between arithmetic and geometric sequences?

Other A Level Maths questions

How do I differentiate y=x^x?

The points A and B have position vectors 2i + 6j – k and 3i + 4j + k respectively. The line l passes through both A and B. Find a vector equation for the line l.

Find the values of x, where 0 < x < 360, such that x solves the equation: 8(tan[x])^2 – 5(sec[x])^2 = 7 + 4sec[x]

Solve the equation 5^x = 8, giving your answer to 3 significant figures.

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss