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)

Answered by Ryan J. Maths tutor

6194 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

SOLVE THE FOLLOWING SIMULTANEOUS EQUATIONS: 5x^2 + 3x - 3y = 4, -4x - 6y + 5x^2 = -7


Differentiate 5x^2+5y^2-6xy=13 to find dy/dx


(Follow on from previous question) A curve has equation y= x^2+3x+2. Use your previous results to i) find the vertex of the curve ii) find the equation of the line of symmetry of the curve


What is the centre and radius of the circle x^2+y^2-6x+4y=-4


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