Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In Problems 25–32, use the given functions f and g.
$(a) f (x) = 0 (b) g (x) = 0 (c) f (x) = g (x) (d) f (x) > 0$
$(e) g (x) \leq 0 (f) f (x) > g (x) (g) f (x) \geq 1$
$f (x) = - x^{2} + 3 g (x) = - 3 x + 3$

The required solution sets are

(a) $x = - \sqrt{3}, \sqrt{3}$

(b) $x = 1$

(d) $\{x : - \sqrt{3} < x < \sqrt{3}\}$

(e) $x \geq 1$

(f) $\{x : 0 < x < 3\}$

(g) $\{x : - \sqrt{2} \leq x \leq \sqrt{2}\}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1. Given information

The given functions are $f (x) = - x^{2} + 3 g (x) = - 3 x + 3$ .
The equation is $f (x) = - x^{2} + 3 g (x) = - 3 x + 3$ .

Part (a) Step 2: Plot the graph and observe

Plot the graph of the function.

From the graph, it can be observed that $f (x) = 0$ when $x = - \sqrt{3}, \sqrt{3}$ .

Part (b) Step 1. Given information

The given functions are $f (x) = - x^{2} + 3 g (x) = - 3 x + 3$
The equation is $g (x) = 0$ .

Part (b) Step 2. Plot the function and observe

Plot the line in the graph obtained for the first function.

From the graph, it can be observed that $g (x) = 0$ when $x = 1$ .

Part (c) Step 1. Given information

The given functions are $f (x) = - x^{2} + 3 g (x) = - 3 x + 3$
The equation is $f (x) = g (x)$ .

Part (c) Step 2. Read the Graph

For $f (x) = g (x)$ , the curves of both the functions must intersect.
From the graph, it can be observed that the functions intersect at $(0, 3) a n d (3, - 6)$ .
So, $f (x) = g (x)$ at $x = 0, 3$ .

Part (d) Step 1. Given information

The given functions are $f (x) = - x^{2} + 3 g (x) = - 3 x + 3$
The inequality is $f (x) > 0$ .

Part (d) Step 2.Find the region above the horizontal axis.

The inequality holds when the curve of the function is above the horizontal axis.
According to the graph obtained in step 2 of part (b), the curve is above the horizontal axis when $- \sqrt{3} < x < \sqrt{3}$ .
So, the solution set is $\{x : - \sqrt{3} < x < \sqrt{3}\}$ .

Part (e) Step 1. Given information

The given functions are $f (x) = - x^{2} + 3 g (x) = - 3 x + 3$
The inequality is $g (x) \leq 0$ .

Part (e) Step 2. Find the region on or below the horizontal axis.

$g (x) \leq 0$ when the line of the function is on or below the horizontal axis.
From the graph, the line is on or below the axis for $x \geq 1$ .

Part (f) Step 1. Given information

The given functions are $f (x) = - x^{2} + 3 g (x) = - 3 x + 3$
The inequality is $f (x) > g (x)$ .

Part (f) Step 2. Read the graph

The inequality holds when the curve lies above the line on the graph.
From the graph, it can be observed that the curve is above the line when $0 < x < 3$ .
So, the solution set of the inequality is $\{x : 0 < x < 3\}$ .

Part (g) Step 1. Given information

The given functions are $f (x) = - x^{2} + 3 g (x) = - 3 x + 3$
The inequality is $f (x) \geq 1$ .

Part (g) Step 2. Read the graph

The inequality holds when the curve lies above the value 1 on the vertical axis.
From the graph, the curve is above 1 when $- \sqrt{2} \leq x \leq \sqrt{2}$ .
So, the solution set of the inequality is $\{x : - \sqrt{2} \leq x \leq \sqrt{2}\}$ .

Find Study Materials for

Create Study Materials

Select your language

Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 25–32, use the given functions f and g.
$(a) f (x) = 0 (b) g (x) = 0 (c) f (x) = g (x) (d) f (x) > 0$
$(e) g (x) \leq 0 (f) f (x) > g (x) (g) f (x) \geq 1$
$f (x) = - x^{2} + 3 g (x) = - 3 x + 3$

Step by Step Solution

Part (a) Step 1. Given information

Part (a) Step 2: Plot the graph and observe

Part (b) Step 1. Given information

Part (b) Step 2. Plot the function and observe

Part (c) Step 1. Given information

Part (c) Step 2. Read the Graph

Part (d) Step 1. Given information

Part (d) Step 2.Find the region above the horizontal axis.

Part (e) Step 1. Given information

Part (e) Step 2. Find the region on or below the horizontal axis.

Part (f) Step 1. Given information

Part (f) Step 2. Read the graph

Part (g) Step 1. Given information

Part (g) Step 2. Read the graph

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 25–32, use the given functions f and g.(a) f(x)=0(b) g(x)=0(c) f(x)=g(x)(d)f(x)>0(e) g(x)≤0(f) f(x)>g(x)(g) f(x)≥1f(x) = -x2+3g(x)=-3x+3

Step by Step Solution

Part (a) Step 1. Given information

Part (a) Step 2: Plot the graph and observe

Part (b) Step 1. Given information

Part (b) Step 2. Plot the function and observe

Part (c) Step 1. Given information

Part (c) Step 2. Read the Graph

Part (d) Step 1. Given information

Part (d) Step 2.Find the region above the horizontal axis.

Part (e) Step 1. Given information

Part (e) Step 2. Find the region on or below the horizontal axis.

Part (f) Step 1. Given information

Part (f) Step 2. Read the graph

Part (g) Step 1. Given information

Part (g) Step 2. Read the graph

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

In Problems 25–32, use the given functions f and g.
$(a) f (x) = 0 (b) g (x) = 0 (c) f (x) = g (x) (d) f (x) > 0$
$(e) g (x) \leq 0 (f) f (x) > g (x) (g) f (x) \geq 1$
$f (x) = - x^{2} + 3 g (x) = - 3 x + 3$