Question

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

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

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

Short answer

(a) $[-2,1]$

(b)$(-\infty ,-3]or[1,\infty )$

Step-by-step solution

Part (a) Step 1. Given Information   

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

Part (a) Step 2. Observe the graph   

• From the graph, it is observed that the value of $f\left(x\right)$is less than $g\left(x\right)$for $-3<x<1$.
• In set builder form, for $f\left(x\right)<g\left(x\right)$, $\left\{x\right|-3<x<1\}$. Also, in interval notation it is denoted as$(-3,1)$.

Part (b) Step 1. Given Information    

It is given that $f\left(x\right)\ge g\left(x\right)$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 or equal to $g\left(x\right)$for role="math" localid="1646315317778" $x\le -3orx\ge 1$.
• In the set builder form, for $f\left(x\right)\ge g\left(x\right)$, role="math" localid="1646315330982" $\left\{x\right|x\le -3orx\ge 1\}$. Also, in interval notation it is denoted asrole="math" localid="1646315359419" $(-\infty ,-3]or[1,\infty )$.