MYTUTOR SUBJECT ANSWERS

436 views

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).
Example:
f(x)=2x+1
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=2y+1                                                                
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...

2 years ago

Answered by Ryan, an A Level Maths tutor with MyTutor


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

253 SUBJECT SPECIALISTS

£24 /hr

Osian S.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I'm Osian, a Master's student at the University of Warwick. I've had fun with mathematics from a young age, and I hope to be able to instill this passion for mathematics in you, through my tutorials! Throughout my time at Warwick,...”

£20 /hr

Sam C.

Degree: Physics with Astrophysics (Masters) - Bath University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Design & Technology

“About Me: I’m currently studying Physics and Astrophysics and the University of Bath. I have prior tutoring experience as well as 2 years teaching regular classes as part of the Combined Cadet Force. I have a real passion for my subje...”

£36 /hr

Gregory D.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“About Me:I recently graduated from the University of Warwick with a 2:1 in Mathematics. I love doing and teaching maths and hope that my tutorials will instil that love in you, too.I am very patient and friendly. I have been tuto...”

About the author

Ryan J.

Currently unavailable: for new students

Degree: Mathematics (Bachelors) - Durham University

Subjects offered: Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.STEP.

“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

What is exactly differentiation?

Integrate (x^3 - x^2 - 5x + 7) with respect to x.

Finding stationary points

What is a stationary point on a curve? How do I calculate the co-ordinates of a stationary point?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok