/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 78. In Problems 71鈥� 86, use the gi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q 78. (page 298)

In Problems 71鈥� 86, use the given functionf to:

(a) Find the domain of f.

(b) Graph f.

(c) From the graph, determine the range and any asymptotes of f.

(d) Find f-1, the inverse of f.

(e) Find the domain and the range of f-1.

(f) Graph f-1.

fx=12logx-5

Short Answer

Expert verified

Part (a) 0,鈭�.

Part (b)

Part (c) Range -5,鈭�and vertical asymptote x=-5.

Part (d) f-1x=102x+10.

Part (e) Domain -鈭�,鈭�and range -5,鈭�.

Part (f)

Step by step solution

01

Part (a) Step 1. Given information.

The given function is:

fx=12logx-5

02

Part (a) Step 2. Find the domain of f.

fx=12logx-5

The domain off consists of all x for which x>0.


Therefore, the domain of the given function is0,鈭�.

03

Part (b) Step 1. Graph f.

Sketch the graph off:

04

Part (c) Step 1. Determine the range and any asymptotes of f  from the graph.

We can see from the graph of f that the range of the function fx=12logx-5is the set of all real numbers.

Therefore, the range of the function is -5,鈭�.


The vertical asymptote of the given function isx=-5.

05

Part (d) Step 1. Find f-1.

fx=12logx-5

For f-1replace fxwithy,

y=12logx-5x=12logy-512logy=x+5logy=2x+10y=102x+10

Therefore, the inverse of f is f-1x=102x+10.

06

Part (e) Find the domain and the range of f-1.

We know that the domain of a functionf(x)is the range of its inverse.

In the same way, the range of a function f(x) is the domain of its inverse.

Therefore, the domain off-1is-鈭�,鈭�and its range is-5,鈭�.

07

Part (f) Graph f-1.

Sketch the graph of f-1:

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=2x+3x+2

Use the graph of y=f(x)given in the Problem 43to evaluate the following:

(a) f(-1)

(b) f(1)

(c) f-1(1)

(d) f-1(2)

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=e-x

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=2x3x-1

Solve the equation2-x=16

and verify your results using a graphing utility
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.