/*! 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. 63 If f(x)=ax+b聽and g(x)=cx+d, the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 63 (page 257)

If f(x)=ax+band g(x)=cx+d, then find: -

(a)f鈭�g

(b)g鈭�f

(c)the domain of f鈭�gand g鈭�f

(d)the conditions for whichf鈭�g=g鈭�f

Short Answer

Expert verified

(a)f鈭�g(x)=acx+ad+b

(b)g鈭�f(x)=acx+bc+d

(c)Domain of f鈭�gand g鈭�fare same, that is set of real numbers.

(d)f鈭�gand g鈭�fare same ifad+b=bc+d.

Step by step solution

01

Step 1. Given Information

Given thatf(x)=ax+bandg(x)=cx+d.

02

Part (a) step 1. solution

we know that f鈭�g(x)=f(g(x)).

Here, f(x)=ax+b, g(x)=cx+d.

then,

f鈭�g(x)=f(g(x))f鈭�g(x)=a(g(x))+bf鈭�g(x)=a{cx+d}+bf鈭�g(x)=acx+ad+b

03

Part (b) Step 1. Solution

We know that g鈭�f(x)=g(f(x)).

Here, f(x)=ax+b, g(x)=cx+d

g鈭�f(x)=g(f(x))g鈭�f(x)=c(f(x))+dg鈭�f(x)=c{ax+b}+dg鈭�f(x)=acx+bc+d

04

Part (c) Step 1. Solution

Since the domain of f(x)and g(x)are set of real number so domain of f鈭�gand g鈭�fare also set of real number.

05

Part (d) Step 1. Solution

We know that f鈭�g(x)=acx+ad+band g鈭�f(x)=acx+bc+d.

Now,

localid="1646279876516" f鈭�g(x)=g鈭�f(x)acx+ad+b=acx+bc+d

Compare coefficients on both sides.

ad+b=bc+d.

So,f鈭�g=g鈭�f

if,ad+b=bc+d.

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

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

fx=ex-1

Use transformations to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=1-2-x/3

If f(7)=3 and f is one-to-one, what isf-1(13)?

A function fhas an inverse function. If the graph of f lies in quadrant II, in which quadrant does the graph of f-1lie?

Solve the equation(15)x=125

and verify your results using a graphing utility.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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.