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)

RJ
Answered by Ryan J. Maths tutor

6300 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What are the roots of 3x^2 + 13x + 4 ?


Given that y=((3x+1)^2)*cos(3x), find dy/dx.


Differentiate the following equation: f(x) = 5x^3 + 6x^2 - 12x + 4


Find dy/dx where y= x^3(sin(x))


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences