Question

In problems 3-6, use the figure to solve each inequality.

a) $g\left(x\right)\ge f\left(x\right)$

b)$f\left(x\right)>g\left(x\right)$

Short answer

(a)$[-2,1]$

(b) $(-\infty ,-2)or(1,\infty )$

Step-by-step solution

Part (a) Step 1. Given Information  

It is given that $g\left(x\right)\ge f\left(x\right)$and the graph is,

Part (a) Step 2. Observe the graph  

• From the graph, it is observed that the value of $g\left(x\right)$is greater than or equal to $f\left(x\right)$for localid="1646313863885" role="math" $-2\le x\le 1$.
• In the set builder form, for $g\left(x\right)\ge f\left(x\right)$, localid="1646313876888" role="math" $\left\{x\right|-2\le x\le 1\}$. Also, in interval notation it is denoted as $[-2,1]$.

Part (b) Step 1. Given Information   

It is given that, $f\left(x\right)>g\left(x\right)$and the graph is,

Part (b) Step 2. Observe the graph   

• From the graph, it is observed that the value of $f\left(x\right)$is greater than $g\left(x\right)$for $x<-2orx>1$.
• In the set builder form, for$f\left(x\right)>g\left(x\right)$,$\left\{x\right|x<-2orx>1\}$. Also, in interval notation it is denoted as role="math" localid="1646313809222" $(-\infty ,-2)or(1,\infty )$.