Q. 30 Suppose that f(x)=3x+5and 聽g(x)... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 3: Q. 30 (page 137)

Suppose that $f (x) = 3 x + 5$ and $g (x) = - 2 x + 15$
(a) Solve $f (x) = 0$ (b) Solve $f (x) < 0$
(c) Solve $f (x) = g (x)$ (d) Solve $f (x) 鈮� g (x)$
(e) Graph $y = f (x)$ and $y = g (x)$ and label the point that represents the solution to the equation $f (x) = g (x)$ .

Short Answer

Expert verified

Part (a) $x = - \frac{5}{3}$

Part (b) $x < - \frac{5}{3}$

Part (c) $x = 2$

Part (d) $x 鈮� 2$

Part (e) Point of intersection is $(2, 11)$

Step by step solution

Part (a). Step 1. Given Information.

There are two functions $f (x) = 3 x + 5$ and $g (x) = - 2 x + 15$ .

Part (a). Step 2. Explanation.

Solve $f (x) = 0$

we have $f (x) = 3 x + 5$

role="math" localid="1646289675009" $3 x + 5 = 0 3 x = - 5 x = - \frac{5}{3}$

Part (a). Step 3. Conclusion

At $x = - \frac{5}{3}$ , $f (x) = 0$

Part (b). Step 1. Explanation

To solve $f (x) < 0$

We have

$3 x + 5 < 0 3 x < - 5 x < - \frac{5}{3}$

Part (b). Step 2. Conclusion.

For $x < - \frac{5}{3}$ , $f (x) < 0$

Part (c). Step 1. Explanation

To solve $f (x) = g (x)$

We have $f (x) = 3 x + 5$ and $g (x) = - 2 x + 15$

$3 x + 5 = - 2 x + 15 3 x + 2 x = 15 - 5 5 x = 10 x = 2$

Part (c). Step 2. Conclusion.

For $x = 2$ , $f (x) = g (x)$

Part (d). Step 1. Explanation

To solve $f (x) 鈮� g (x)$

$3 x + 5 鈮� - 2 x + 15 5 x 鈮� 10 x 鈮� 2$

Part (d). Step 2. Conclusion.

As $x 鈮� 2$ , $f (x) 鈮� g (x)$

Part (e). Step 1. Explanation.

Make the table for $y = f (x)$

x	$y = 3 x + 5$
-2	-1
0	5
2	11

Make the table for $y = g (x)$

x	$y = - 2 x + 15$
-2	19
0	15
2	11

the point that represents the solution to the equation $f (x) = g (x)$ is intersection of graphs $f (x), g (x)$ .

Part (e). Step 2. Conclusion.

The graph is as below and the point that represents the solution to the equation $f (x) = g (x)$ is $(2, 11)$

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91影视

Suppose that $f (x) = 3 x + 5$ and $g (x) = - 2 x + 15$
(a) Solve $f (x) = 0$ (b) Solve $f (x) < 0$
(c) Solve $f (x) = g (x)$ (d) Solve $f (x) 鈮� g (x)$
(e) Graph $y = f (x)$ and $y = g (x)$ and label the point that represents the solution to the equation $f (x) = g (x)$ .

Short Answer

Step by step solution

Part (a). Step 1. Given Information.

Part (a). Step 2. Explanation.

Part (a). Step 3. Conclusion

Part (b). Step 1. Explanation

Part (b). Step 2. Conclusion.

Part (c). Step 1. Explanation

Part (c). Step 2. Conclusion.

Part (d). Step 1. Explanation

Part (d). Step 2. Conclusion.

Part (e). Step 1. Explanation.

Part (e). Step 2. Conclusion.

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91影视

Suppose that f(x)=3x+5and g(x)=-2x+15(a) Solve f(x)=0 (b) Solve f(x)<0(c) Solve f(x)=g(x) (d) Solve f(x)鈮�g(x)(e) Graph y=f(x)and y=g(x)and label the point that represents the solution to the equation f(x)=g(x).

Short Answer

Step by step solution

Part (a). Step 1. Given Information.

Part (a). Step 2. Explanation.

Part (a). Step 3. Conclusion

Part (b). Step 1. Explanation

Part (b). Step 2. Conclusion.

Part (c). Step 1. Explanation

Part (c). Step 2. Conclusion.

Part (d). Step 1. Explanation

Part (d). Step 2. Conclusion.

Part (e). Step 1. Explanation.

Part (e). Step 2. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Suppose that $f (x) = 3 x + 5$ and $g (x) = - 2 x + 15$
(a) Solve $f (x) = 0$ (b) Solve $f (x) < 0$
(c) Solve $f (x) = g (x)$ (d) Solve $f (x) 鈮� g (x)$
(e) Graph $y = f (x)$ and $y = g (x)$ and label the point that represents the solution to the equation $f (x) = g (x)$ .