Q 30. - Precalculus Enhanced with Graphing Utilities

Question

Find the inverse of one-to-one function. State the domain and the range of inverse function. $\left\{\left(-2,2\right), \left(-1,6\right), \left(0,8\right), \left(1,-3\right), \left(2,9\right)\right\}$

Step-by-Step Solution

Answer

Inverse of given function is $\left\{\left(2,-2\right), \left(6,-1\right), \left(8,0\right), \left(-3,1\right), \left(9,2\right)\right\}$

Domain of inverse function is $\left\{2, 6, 8, -3, 9\right\}$

Range of inverse function is $\left\{-2, -1, 0, 1, 2\right\}$

Step 1. Definition of inverse function

The function is one-to-one. To find the inverse function, we interchange the elements in the domain with the elements in the range.  

The inverse of given function is $\left\{\left(2,-2\right), \left(6,-1\right), \left(8,0\right), \left(-3,1\right), \left(9,2\right)\right\}$

Step 2. Domain of inverse function

The domain of the inverse function is $\left\{2, 6, 8, -3, 9\right\}$

Step 3. Range of inverse function

The range of inverse function is $\left\{-2, -1, 0, 1, 2\right\}$