Chapter 3: Q. 3 (page 171)

In problems 3-6, use the figure to solve each inequality.
a) $f (x) > 0$
b) $f (x) \leq 0$

Short Answer

Expert verified

a) $(- \infty, - 2)$ or $(2, \infty)$

b) $[- 2, 2]$

Step by step solution

Part (a) Step 1. Given Information

It is given that, $f (x) > 0$ and the graph is,

Part (a) Step 2. Observe the graph

From the graph, it is observed that the value of $y$ or $f (x)$ is positive for role="math" localid="1646049546322" $x < - 2$ or $x > 2$ .
In set builder form, for $f (x) > 0$ , $\{x | x < - 2 o r x > 2\}$ . Also, in interval notation it is denoted as $(- \infty, - 2) o r (2, \infty)$ .

Part (b) Step 1. Given Information

It is given that, $f (x) \leq 0$ and the graph is,

Part (b) Step 2. Observe the graph

From the graph, it is observed that the value of $y = f (x)$ is negative or equal to 0 for $- 2 \leq x \leq 2$ .
In set builder form, for $f (x) \leq 0$ , ${x | - 2 \leq x \leq 2}$ . Also, in interval notation it is denoted as $[- 2, 2]$ .

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In problems 3-6, use the figure to solve each inequality.
a) $f (x) > 0$
b) $f (x) \leq 0$

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Observe the graph

Part (b) Step 1. Given Information

Part (b) Step 2. Observe the graph

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In problems 3-6, use the figure to solve each inequality.a) f(x)>0b)f(x)≤0

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Observe the graph

Part (b) Step 1. Given Information

Part (b) Step 2. Observe the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In problems 3-6, use the figure to solve each inequality.
a) $f (x) > 0$
b) $f (x) \leq 0$