Question

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

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

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

Short answer

Part a. The solution of the inequality $f\left(x\right)>0$is role="math" localid="1646170593198" $(-\infty ,-1)\cup (-1,1)\cup (3,\infty )$.

Part b. The solution of the inequality$f\left(x\right)\le 0$is $[1,2)\cup (2,3]$.

Step-by-step solution

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

From the graph, we can see two intervals $x<1$and $x>3$, for which the graph is below the x axis. Also the function is not defined for$x=-1$and$x=2$.

So the solution is given as $(-\infty ,-1)\cup (-1,1)\cup (3,\infty )$.

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

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

From the graph, we can see that for the interval$\left[1,3\right]$ the graph is below the x axis. The function is not defined for$x=-1$and $x=2$.

So the solution is given as $[1,2)\cup (2,3]$.