Chapter 4.7, Problem 1CYU

To determine

To find: The inverse of the relation $\left\{\left(4,-15\right),\left(-8,-18\right),\left(-2,-16.5\right),\left(3,-15.25\right)\right\}$ .

Answer to Problem 1CYU

The inverse of the relation $\left\{\left(4,-15\right),\left(-8,-18\right),\left(-2,-16.5\right),\left(3,-15.25\right)\right\}$ is $\left\{\left(-15,4\right),\left(-18,-8\right),\left(-16.5,-2\right),\left(-15.25,-3\right)\right\}$ .

Explanation of Solution

Given:

The relation is $\left\{\left(4,-15\right),\left(-8,-18\right),\left(-2,-16.5\right),\left(3,-15.25\right)\right\}$ .

Calculation:

Exchange the x and y coordinates of the given relation $\left\{\left(4,-15\right),\left(-8,-18\right),\left(-2,-16.5\right),\left(3,-15.25\right)\right\}$ to obtain the inverse.

$\begin{array}{c}\left(4,-15\right)\to \left(-15,4\right)\\ \left(-8,-18\right)\to \left(-18,-8\right)\\ \left(-2,-16.5\right)\to \left(-16.5,-2\right)\\ \left(3,-15.25\right)\to \left(-15.25,3\right)\end{array}$

Thus, the inverse of the given relation is $\left\{\left(-15,4\right),\left(-18,-8\right),\left(-16.5,-2\right),\left(-15.25,-3\right)\right\}$ .