Q. 31 In Problems 25鈥�32, use the giv... [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. 31 (page 171)

In Problems 25鈥�32, use the given functions f and g.
(a) Solve $f (x) = 0$ .
(b) Solve $g (x) = 0$ .
(c) Solve $f (x) = g (x)$ .
(d) Solve $f (x) > 0$ .
(e) Solve $g (x) 鈮� 0$ .
(f) Solve $f (x) > g (x)$ .
(g) Solve $f (x) 鈮� 1$ .
$f (x) = x^{2} - x - 2 g (x) = x^{2} + x - 2$

Short Answer

Expert verified

(a) Solution of $f (x) = 0$ is $x = - 1 & 2$

(b) Solution of $g (x) = 0$ is $x = - 2 & 1$

(d) Solution of $f (x) > 0$ is $(- 鈭�, - 1) 鈭� (2, 鈭�)$

(e) Solution of $g (x) 鈮� 0$ is $[- 2, 1]$

(f) Solution of $f (x) > g (x)$ is $(- 鈭�, 0)$

(g) Solution of $f (x) 鈮� 1$ is $(- 鈭�, - 1.3] 鈭� [2.3, 鈭�)$

Step by step solution

Step 1. Given information

The given functions are

$f (x) = x^{2} - x - 2 g (x) = x^{2} + x - 2$

Step 2. Part (a)

Substitute zero for function value in function $f (x)$

localid="1647294466594" $f (x) = x^{2} - x - 2 0 = x^{2} - x - 2 0 = (x + 1) (x - 2) x = - 1 & 2$

So $f (x) = 0$ at $x = - 1 & 2$

Step 3. Part (b)

Substitute zero for function value in function $g (x)$

$g (x) = x^{2} + x - 2 0 = x^{2} + x - 2 0 = (x - 1) (x + 2) x = 1 & - 2$

So $g (x) = 0$ at $x = - 2 & 1$

Step 4. Part (c)

Equate both functions

$f (x) = g (x) x^{2} - x - 2 = x^{2} + x - 2 - x = x x = 0$

So $f (x) = g (x)$ at $x = 0$

Step 5. Pard (d)

Plot the graph of $f (x) = x^{2} - x - 2$

The graph state that the $f (x) > 0$ at $(- 鈭�, - 1) 鈭� (2, 鈭�)$

Step 6. Part (e)

Plot the graph of $g (x) = x^{2} + x - 2$

The graph state that the solution of $g (x) 鈮� 0$ is $[- 2, 1]$

Step 7. Part (f)

Plot the graph of $f (x) & g (x)$

The graph state that the solution of $f (x) > g (x)$ is $(- 鈭�, 0)$

Step 8. Part (g)

Plot the graph of $f (x)$ and $y = 1$

The graph state that the solution of $f (x) 鈮� 1$ is $(- 鈭�, - 1.3] 鈭� [2.3, 鈭�)$

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91影视

In Problems 25鈥�32, use the given functions f and g.
(a) Solve $f (x) = 0$ .
(b) Solve $g (x) = 0$ .
(c) Solve $f (x) = g (x)$ .
(d) Solve $f (x) > 0$ .
(e) Solve $g (x) 鈮� 0$ .
(f) Solve $f (x) > g (x)$ .
(g) Solve $f (x) 鈮� 1$ .
$f (x) = x^{2} - x - 2 g (x) = x^{2} + x - 2$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Part (a)

Step 3. Part (b)

Step 4. Part (c)

Step 5. Pard (d)

Step 6. Part (e)

Step 7. Part (f)

Step 8. Part (g)

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91影视

In Problems 25鈥�32, use the given functions f and g.(a) Solve f(x)=0.(b) Solve g(x)=0.(c) Solve f(x)=g(x).(d) Solve f(x)>0.(e) Solve g(x)鈮�0.(f) Solve f(x)>g(x).(g) Solve f(x)鈮�1.f(x)=x2-x-2g(x)=x2+x-2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Part (a)

Step 3. Part (b)

Step 4. Part (c)

Step 5. Pard (d)

Step 6. Part (e)

Step 7. Part (f)

Step 8. Part (g)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 25鈥�32, use the given functions f and g.
(a) Solve $f (x) = 0$ .
(b) Solve $g (x) = 0$ .
(c) Solve $f (x) = g (x)$ .
(d) Solve $f (x) > 0$ .
(e) Solve $g (x) 鈮� 0$ .
(f) Solve $f (x) > g (x)$ .
(g) Solve $f (x) 鈮� 1$ .
$f (x) = x^{2} - x - 2 g (x) = x^{2} + x - 2$