Inverse of a Function
How to find inverse of a function?

If f(x) is a function then its inverse f -1(x) can be found by following steps:

  1. Replace f(x) by y
  2. Replace y by x, and x by y
  3. Solve for y
  4. Replace y by f -1(x)

Related Questions:

Q. If f(x)=2x-3, then f -1(x)=?
Solution:

f(x)=2x-3
Step-1. Replace f(x) by y
y=2x-3
Step-2. Replace y by x, and x by y
x=2y-3
Step-3. Solve for y
x+3=2y

Step-4. Replace y by f -1(x)

Which is the inverse of the given function.


Q. Find inverse of the function:

Solution:

Step-1. Replace f(x) by y

Step-2. Replace y by x, and x by y

Step-3. Solve for y
y+2=3x
y=3x-2

Step-4. Replace y by f -1(x)
f -1(x)=3x-2
Which is the inverse of the given function.