/*! 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. 76 If f and g are odd functions, sh... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 76 (page 258)

If f and g are odd functions, show that the composite function f鈭�g is also odd.

Short Answer

Expert verified

The, f鈭�gis an odd function.

Step by step solution

01

Step 1. Given Information

Given that fand gare odd functions.

02

Step 2. Explanation

A function fis said to be odd function if f(-x)=-f(x),鈭赌x.

Since, fand gare odd function, So

f(-x)=-f(x)g(-x)=-g(x)

Now,

f鈭�g(x)=f(g(x))

then,

f鈭�g(-x)=f(g(-x))f鈭�g(-x)=f(-g(x)){gisoddfunction.}f鈭�g(-x)=-f(g(x)){fisoddfunction.}f鈭�g(-x)=-f鈭�g(x)鈭赌x

Hence,f鈭�gis an odd function.

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

Solve the equation 5x+3=15

and verify your results using a graphing utility.

solve each equation. Verify your results using a graphing utility.

5x2+8=1252x

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

A(n)________ is a function of the form f(x)=Caxwhere a>0,a鈮�1,and C鈮�0are real numbers. The base ais a ____ and C is a _____.

True or Falsefgx=fx.gx.

The graph of an exponential function is given. Match each graph to one of the following functions.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.