MYTUTOR SUBJECT ANSWERS

742 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

351 SUBJECT SPECIALISTS

£26 /hr

Luke B.

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Maths, Further Mathematics + 3 more

Maths
Further Mathematics
.STEP.
.MAT.
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£24 /hr

Jaisal P.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hello, my name is Jaisal. I'm studying Maths at Durham University, and I'm here to help you improve your Maths.”

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

Prove the following identity: (1+cos⁡(x)+cos⁡(2x))/(sin⁡(x)+sin⁡(2x) )=cot⁡(x)

What is the integral of x sin(x) dx?

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

How do I integrate terms with sin^2(x) and cos^2(x) in them? For example integrate (1+sin(x))^2 with respect to x

View A Level Maths tutors

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

mtw:mercury1:status:ok