Chapter 4: Q. 8 (page 241)

Use the graph of the function f to solve the inequality.
(a) $f (x) > 0$
(b) $f (x) \leq 0$

Short Answer

Expert verified

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

Part b. The solution of the inequality $f (x) \leq 0$ 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 $f (x) > 0$ , 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 $f (x) \leq 0$ , 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 $[1, 3]$ the graph is below the x axis. The function is not defined for $x = - 1$ and $x = 2$ .

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

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Use the graph of the function f to solve the inequality.
(a) $f (x) > 0$
(b) $f (x) \leq 0$

Short Answer

Step by step solution

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

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

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Use the graph of the function f to solve the inequality. (a)f(x)>0(b)f(x)≤0

Short Answer

Step by step solution

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Use the graph of the function f to solve the inequality.
(a) $f (x) > 0$
(b) $f (x) \leq 0$