Chapter 4.4, Problem 8AYU

In Problems 5-8, use the graph of the function $f$ to solve the inequality.

(a) $f\left(x\right)>0$

(b) $f\left(x\right)\le 0$

To determine

To find: The inequality by using the graph of the function.

a. $f\left(x\right)<0$

Answer to Problem 8AYU

a. $\left\{x|1\le x<2\text{ or }2<x\le 2\right\}$

Explanation of Solution

Given:

a. From the graph, we can see that $f\left(x\right)<0$ for $1\le x<2$ or $2<x\le 3$. The solution set is $\left\{x|1\le x<2\text{ or }2<x\le 2\right\}$ or, using interval notation, $\left[1,2\right)\cup \left(2,3\right]$.

To determine

To find: The inequality by using the graph of the function.

b. $f\left(x\right)\ge 0$

Answer to Problem 8AYU

b. $\left\{x|x<-1\text{ or }-1<x<1\text{ or }x>3\right\}$

Explanation of Solution

Given:

b. From the graph, we can see that $f\left(x\right)\text{ > }0$ for $-\infty <x<-1$ or $-1<x<1$ or $x>3$. The solution set is $\left\{x|x<-1\text{ or }-1<x<1\text{ or }x>3\right\}$ or, using interval notation, $\left(-\infty ,-1\right)\cup \left(-1,1\right)\cup \left(3,\infty \right)$.