Q. 10 The function fx=5x+2聽is one to ... [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 11: Q. 10 (page 796)

The function $f (x) = \frac{5}{x + 2}$ is one to one. Find $f^{- 1}$ . Find the domain and the range of $f$ and the domain and the range of $f^{- 1}$ .

Short Answer

Expert verified

$f^{- 1} = \frac{5 - 2 x}{x}$

The domain of $f$ is defined for all values of $x$ except for $x = - 2$ and its range is, all the real numbers.

The domain of $f^{- 1}$ is defined for all values of $x$ except for $x = 0$ and the range is all the real numbers.

Step by step solution

Step 1 Given function is,

$f (x) = \frac{5}{x + 2}$ .

Find $f^{- 1}$ .

Solve the given function for $x$ .

$f (x) = \frac{5}{x + 2} f (x) (x + 2) = 5 x f (x) + 2 f (x) = 5 x f (x) = 5 - 2 f (x) x = \frac{5 - 2 f (x)}{f (x)}$

Step 2 Now substitute fx=x,x=f-1in the obtained equation.

$f^{- 1} = \frac{5 - 2 x}{x}$

The domain of $f (x)$ is defined for all values of $x$ except for $x = - 2$ and the given function can take up any of the values in the range of real numbers . So, the range of $f$ is all the real numbers.

The domain of $f^{- 1}$ is defined for all the values of $x$ except for $x = 0$ and the given function can take up any of the values in the range of real numbers . So, the range of $f^{- 1}$ is all the real numbers.

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91影视

The function $f (x) = \frac{5}{x + 2}$ is one to one. Find $f^{- 1}$ . Find the domain and the range of $f$ and the domain and the range of $f^{- 1}$ .

Short Answer

Step by step solution

Step 1 Given function is,

Step 2 Now substitute fx=x,x=f-1in the obtained equation.

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91影视

The function fx=5x+2is one to one. Find f-1. Find the domain and the range of fand the domain and the range of f-1.

Short Answer

Step by step solution

Step 1 Given function is,

Step 2 Now substitute fx=x,x=f-1in the obtained equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Mechanics Maths

Logic and Functions

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

The function $f (x) = \frac{5}{x + 2}$ is one to one. Find $f^{- 1}$ . Find the domain and the range of $f$ and the domain and the range of $f^{- 1}$ .