Chapter 8.1, Problem 21WE

To determine

To prove that $g\left(a+c\right)=g\left(a\right)+g\left(c\right)$

Explanation of Solution

Given information:

The given statement is:

“Prove that if $g$ is a direct variation over the real numbers, then for every pair of real numbers $a\text{ and }c$ .”

  $g\left(a+c\right)=g\left(a\right)+g\left(c\right)$

Proof:

If $g$ is a direct variation over the real numbers, then it increases with the increase in real number and decreases with the decrease in real number. From the distributive law it is seen that:

  $g\left(a+c\right)=g\left(a\right)+g\left(c\right)$

Hence, the given variation is proved.