Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 2: Q. 74 (page 69)

Given $f (x) = \frac{1}{x}$ and $(\frac{f}{g}) (x) = \frac{x + 1}{x^{2} - x}$ ,find the function $g$ .

Short Answer

Expert verified

The value of $g (x) = \frac{x - 1}{x + 1}$

Step by step solution

Step 1. Given Information

Given $f (x) = \frac{1}{x}$ and role="math" localid="1646229850323" $(\frac{f}{g}) (x) = \frac{x + 1}{x^{2} - x}$ ,

We have to find the function $g$ .

Step 2. We know that fg(x)=f(x)g(x)Simplifying the formula for g(x)

Multiply with $g (x)$ on both side

$(\frac{f}{g}) (x) 路 g (x) = \frac{f (x)}{g (x)} 路 g (x) (\frac{f}{g}) (x) 路 g (x) = f (x) Divide by (\frac{f}{g}) (x) on both side (\frac{f}{g}) (x) 路 g (x) 路 \frac{1}{(\frac{f}{g}) (x)} = \frac{f (x)}{(\frac{f}{g}) (x)} g (x) = \frac{f (x)}{(\frac{f}{g}) (x)}$

Step 3. Putting the value of f(x) and fg(x)

$g (x) = \frac{\frac{1}{x}}{\frac{x + 1}{x^{2} - x}} g (x) = \frac{1}{x} 路 \frac{x^{2} - x}{x + 1} g (x) = \frac{1}{x} 路 \frac{x (x - 1)}{x + 1} g (x) = \frac{x - 1}{x + 1}$

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91影视

Given $f (x) = \frac{1}{x}$ and $(\frac{f}{g}) (x) = \frac{x + 1}{x^{2} - x}$ ,find the function $g$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. We know that fg(x)=f(x)g(x)Simplifying the formula for g(x)

Step 3. Putting the value of f(x) and fg(x)

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91影视

Given f(x)=1xand fg(x)=x+1x2-x,find the functiong.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. We know that fg(x)=f(x)g(x)Simplifying the formula for g(x)

Step 3. Putting the value of f(x) and fg(x)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Given $f (x) = \frac{1}{x}$ and $(\frac{f}{g}) (x) = \frac{x + 1}{x^{2} - x}$ ,find the function $g$ .