Chapter 14.5, Problem 3ST1

To determine

To find the image and preimage of the origin.

Answer to Problem 3ST1

The image is $\left(1,-2\right)$ and the preimage is $\left(-1,2\right)$ .

Explanation of Solution

Given information:

The given function is:

  $T:\left(x,y\right)=\left(x+1,y-2\right)$

Calculation:

The image can be calculated by:

  $\begin{array}{l}T:\left(x,y\right)=\left(x+1,y-2\right)\\ T:\left(0,0\right)=\left(0+1,0-2\right)=\left(1,-2\right)\end{array}$

The preimage can be calculated by;

  $\begin{array}{l}T:\left(x,y\right)=\left(x+1,y-2\right)\\ x+1=0\\ x=-1\\ y-2=0\\ y=2\end{array}$

Hence, the image is $\left(1,-2\right)$ and the preimage is $\left(-1,2\right)$ .