Q. 29 Suppose that f(x)=4x-1and 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. 29 (page 137)

Suppose that $f (x) = 4 x - 1$ and $g (x) = - 2 x + 5$
(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) $x = \frac{1}{4}$

Part (b) $\{x | x > \frac{1}{4}\}$

Part (c) $x = 1$

Part (d) $\{x | x 鈮� 1\}$

Part (e)

Step by step solution

Part (a). Step 1. Given information.

There are two functions $f (x) = 4 x - 1$ and $g (x) = - 2 x + 5$ .

Part (a). Step 2. Explanation.

To solve $f (x) = 0$ equate the function with 0.

$f (x) = 0 4 x - 1 = 0 4 x = 1 x = \frac{1}{4}$

At $x = \frac{1}{4}$ , $f (x) = 0$ .

Part (b). Step 1. Explanation.

To solve $f (x) > 0$ , We have $f (x) = 4 x - 1$ .

so,

$f (x) > 0 4 x - 1 > 0 4 x > 1 x > \frac{1}{4}$

For all $x > \frac{1}{4}$ , $f (x) > 0$

Part (c). Step 1. Explanation.

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

So,

$f (x) = g (x) 4 x - 1 = - 2 x + 5$

Combine like terms.

$6 x = 6 x = 1$

For $x = 1$ , $f (x) = g (x)$

Part (d). Step 1. Explanation.

To solve $f (x) 鈮� g (x)$ .

So,

$f (x) 鈮� g (x) 4 x - 1 鈮� - 2 x + 5 6 x 鈮� 6 x 鈮� 1$

For all $x 鈮� 1$ , $f (x) 鈮� g (x)$

Part (e). Step 1. Explanation.

Make table for $y = f (x)$

x	$y = 4 x - 1$
-2	-9
0	-1
2	7

Make table for $y = g (x)$

x	$y = - 2 x + 5$
-2	9
0	5
2	1

Graph $y = f (x)$ and $y = g (x)$ and label the point $f (x) = g (x)$

$f (x) = g (x)$ is intersection of graph $f (x)$ and $g (x)$ which is $(1, 3)$

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91影视

Suppose that $f (x) = 4 x - 1$ and $g (x) = - 2 x + 5$
(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 (b). Step 1. Explanation.

Part (c). Step 1. Explanation.

Part (d). Step 1. Explanation.

Part (e). Step 1. Explanation.

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91影视

Suppose that f(x)=4x-1and g(x)=-2x+5(a) Solve f(x)=0. (b) Solve f(x)>0(c) Solve f(x)=g(x) (d) Solve f(x)鈮�g(x)(e) Graphy=f(x)andy=g(x)and label the point that represents the solution to the equationf(x)=g(x).

Short Answer

Step by step solution

Part (a). Step 1. Given information.

Part (a). Step 2. Explanation.

Part (b). Step 1. Explanation.

Part (c). Step 1. Explanation.

Part (d). Step 1. Explanation.

Part (e). Step 1. Explanation.

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Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Suppose that $f (x) = 4 x - 1$ and $g (x) = - 2 x + 5$
(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 $f (x) = g (x)$ .