## Definition Of Inverse Functions

f ^{-1}(x) is said to be the inverse of f(x)

if f(f ^{-1}(x)) = f ^{-1}(f(x)) = x. It is obtained by interchanging the variables x and y of the function.

### More About Inverse Functions

Inverse of a function is the reflection of the function about the line y = x.

Inverse of a function does not necessarily always be a function.

### Video Examples: Inverse Functions - The Basics

### Example of Inverse Functions

y = 3x - 5 is a function where x = 3, 4, 5. y = 3x - 5 = 4, 7, and 10 by substituting the values of x.

Thus, the function is {(3, 4), (4, 7), (5, 10)}.

The inverse of the function is {(4, 3), (7, 4) (10, 5)} by interchanging the first and second co-ordinates.

### Solved Example on Inverse Functions

**Ques: **Find the inverse of the function y = 4x - 7/4.

##### Choices:

A. y = 4x + 3

B. y = 4/4x + 7

C. y = 4x +7/4

D. y = x + 7

Correct Answer: C

### Solution:

Step 1: y = 4x - 7/4.

Step 2: Interchange x and y and find y in terms of x.

Step 3: x = 4y - 7/4 [Interchange x and y.]

Step 4: 4x = 4y - 7 [Multiply throughout by 4.]

Step 5: 4x + 7 = 4y [Add 7 to both sides of the equation.]

Step 6: 4x + 7/4 = y

Step 7: The inverse function is y = 4x + 7/4.