Question

In the following exercises, find the inverse of each function. Determine the domain and range of the inverse function.
$\left\{(5,3),(4,2),(3,1),(2,0)\right\}$.

Short answer

The inverse of the function is $\left\{(3,5),(2,4),(1,3),(0,2)\right\}$.

Domain is $\left\{3,2,1,0\right\}$.

Range is$\left\{5,4,3,2\right\}$.

Step-by-step solution

Step 1. Given and explanation

We have $\left\{(5,3),(4,2),(3,1),(2,0)\right\}$.

Inverse of a function is the order pair as $(y,x)$when the function is one to one function.

The domain is the input value and the range is the output value.

Step 2. Finding the values.

We have $\left\{(5,3),(4,2),(3,1),(2,0)\right\}$.

The inverse of the function will be $\left\{(3,5),(2,4),(1,3),(0,2)\right\}$.

Domain is the input value, i.e. domain is $\left\{3,2,1,0\right\}$.

Range is the output value, i.e. range is$\left\{5,4,3,2\right\}$.