Chapter 5.1, Problem 10MRE

To determine

To find: Solution set of each inequality.

Answer to Problem 10MRE

Solution set of given inequality is $g\le 0$ or $g\ge 1$ .

Explanation of Solution

Given information:

  $g\le g^2$

  $g\le g^2$

  $\begin{array}{l}g\le g^2\\ \Rightarrow g-g\le g^2-g\\ \Rightarrow 0\le g^2-g\\ \Rightarrow g^2-g\ge 0\\ \Rightarrow g\left(g-1\right)\ge 0\\ \Rightarrow \left(g-0\right)\left(g-1\right)\ge 0\end{array}$

If $\left(x-a\right)\left(x-b\right)\ge 0$ and $a<b$ then

  $x\le a$ or $x\ge b$ .

Therefore,

Solution set of given inequality is $g\le 0$ or $g\ge 1$ .