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 $f (x) \leq g (x)$
(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) $\{x | x \leq 1\}$

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 $f (x) \leq g (x)$ .

So,

$f (x) \leq g (x) 4 x - 1 \leq - 2 x + 5 6 x \leq 6 x \leq 1$

For all $x \leq 1$ , $f (x) \leq g (x)$

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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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 $f (x) \leq g (x)$
(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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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)≤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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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Calculus

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Statistics

Theoretical and Mathematical Physics

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 $f (x) \leq g (x)$
(e) Graph $y = f (x)$ and $y = g (x)$ and label the point that represents the solution to the equation $f (x) = g (x)$ .