Chapter 14.7, Problem 23WE

To determine

To find : the rule for $S^{-1}$ .

Answer to Problem 23WE

The $S^{-1}\left(x,y\right)=\left(\frac{x}{3},-2y\right)$ .

Explanation of Solution

Given information : $S:\left(x,y\right)\to \left(3x-\frac{1}{2}y\right)$ .

Calculation :

  $\begin{array}{l}{S}^{-1}\left(S\left(t,z\right)\right)\\ \Rightarrow \left(t,z\right)\\ \Rightarrow S^{-1}\left(3t,-\frac{1}{2}z\right)=\left(t,z\right)\\ \Rightarrow S^{-1}\left(x,y\right)=\left(\frac{x}{3},-2y\right)\end{array}$