Mathematics → Subject Test → 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.