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:
- Replace f(x) by y
- Replace y by x, and x by y
- Solve for y
- 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.