Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

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

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

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

Step-by-Step Solution

Answer

(a) $[-2,1]$

(b) $(-\infty ,-3] or [1,\infty )$

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 $x\le -3 or x\ge 1$.
• In the set builder form, for $f\left(x\right)\ge g\left(x\right)$, $\left\{x\right|x\le -3 or x\ge 1\}$. Also, in interval notation it is denoted as  $(-\infty ,-3] or [1,\infty )$.