Q 29. - Precalculus Enhanced with Graphing Utilities

Question

Find the inverse of one-to-one function. State the domain and the range of inverse function. $\left\{\left(-3,5\right), \left(-2,9\right), \left(-1,2\right), \left(0,11\right), \left(1,-5\right)\right\}$

Step-by-Step Solution

Answer

Inverse of given function is $\left\{\left(5,-3\right), \left(9,-2\right), \left(2,-1\right), \left(11,0\right), \left(-5,1\right)\right\}$

Domain of inverse function is $\left\{5, 9, 2, 11, -5\right\}$

Range of inverse function is $\left\{-3, -2, -1, 0, 1\right\}$

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 $\left\{\left(5,-3\right), \left(9,-2\right), \left(2,-1\right), \left(11,0\right), \left(-5,1\right)\right\}$

Step 2. Domain of inverse function

The domain of the inverse function is $\left\{5, 9, 2, 11, -5\right\}$

Step 3. Range of inverse function

The range of inverse function is $\left\{-3, -2, -1, 0, 1\right\}$