Q 31. - Precalculus Enhanced with Graphing Utilities

Question

Find the inverse of one-to-one function $\left\{\left(-2,1\right),\left(-3,2\right),\left(-10,0\right),\left(1,9\right),\left(2,4\right)\right\}$. State the domain and the range of each inverse function.

Step-by-Step Solution

Answer

Inverse of the function is $\left\{\left(1,-2\right),\left(2,3\right),\left(0,-10\right),\left(9,1\right),\left(4,2\right)\right\}$. Domain and Range of the inverse function is $\left\{1,2,0,9,4\right\}$ and $\left\{-2,-3,-10,1,2\right\}$ respectively.

Step 1. Given information.

Given a one-to-one function $\left\{\left(-2,1\right),\left(-3,2\right),\left(-10,0\right),\left(1,9\right),\left(2,4\right)\right\}$. 

Step 2. Find the inverse of the one-to-one function.

Note that inverse of every one-to-one function exists.

The inverse of the function is found by interchanging the entries in each ordered pair.

Therefore, inverse of the given function is $\left\{\left(1,-2\right),\left(2,3\right),\left(0,-10\right),\left(9,1\right),\left(4,2\right)\right\}$.

Step 3. Find the domain and range of the inverse function.

Domain of a function is the set of all first components in a function.  

Domain of the inverse function is $\left\{1,2,0,9,4\right\}$.

Range of a function is the set of all second components in a function.  

Range of the inverse function is $\left\{-2,3,-10,1,2\right\}$.