What is an inverse Relation?

Answer 1

Definition

A relationship between two numbers in which an increase in the value of one number results in a decrease in the value of the other number.

The inverse of the relation

(2,3), (4,5), (2,6), (4,6)

is

(3,2), (5,4), (6,2), (6,4)

Generally we switch the roles of x and y to find the inverse.

For functions, we follow the steps below to find the inverse:

• Step 1: Switch the x and y.

• Step 2: Solve for y.

• Step 3: Write in inverse notation.

Example

Find the inverse of

y = 2x + 1

Solution

1. We write

   x = 2y + 1

2. We solve:

   x - 1 = 2y

   x - 1

   y =

   2

3. We write

   x - 1

   f -1(x) =

   2

Notice that the original function took x, multiplied by 2 and added 1, while the inverse function took x, subtracted 1 and divided by2. The inverse function does the reverse of the original function in reverse order.