Question

Use the graph of the function f to solve the inequality.

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

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

Short answer

Part a. The solution of the inequality $f\left(x\right)<0$is $(-1,1)\cup (2,\infty )$.

Part b. The solution of the inequality $f\left(x\right)\ge 0$is $(-\infty ,-1]\cup [1,2]$.

Step-by-step solution

Part (a) Step 1. Find the values for which the graph is below the x axis 

To find the solution of $f\left(x\right)<0$, we need to find the values of x for which the graph is below thex axis.

From the graph, we can see two intervals $-1<x<1$and $x>2$, for which the graph is below the x axis.

So the solution is given as $(-1,1)\cup (2,\infty )$.

Part (b) Step 1. Find the values for which the graph is above the x axis 

To find the solution of $f\left(x\right)\ge 0$, we need to find the values of x for which the graph is above the x axis.

From the graph, we can see two intervals $x\le -1$and $1\le x\le 2$, for which the graph is above the x axis.

So the solution is given as $(-\infty ,-1]\cup [1,2]$.