/*! 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 8. If f-1聽denotes the inverse of a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q 8. (page 267)

If f-1denotes the inverse of a function f, then the graphs of f andf-1 are symmetric with respect to the line鈥�鈥�

Short Answer

Expert verified

Iff-1denotes the inverse of a functionf, then the graph offandf-1are symmetric with respect to the liney=x.

Step by step solution

01

Step 1. Definition

The inverse function is a function obtained by reversing the given function. The domain and range of the given function are changed as the range and domain .

02

Step 2. Explanation

If a,bis a point on the graph of a function fthen b,ais a point on the graph of its inverse.

Furthermore, the two graphs will be symmetric about the line y=xhave symmetry when graphed on the same set of axes.

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

Evaluate each expression using the values given in the table.

(a) f鈭�g1(b) f鈭�g2(c) g鈭�f2(d) g鈭�f3(e) g鈭�g1(f) f鈭�f3.

True or Falsefgx=fx.gx.

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

f(x)=-3x+1x

The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

If f(x)=2x2+5and g(x)=3x+a, find a so that the graph of f鈭�g crosses the y-axis at 23.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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.