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Chapter 5: Q. 5 (page 348)

In Problems 5鈥�7, find f o g, g o f, f o f, and g o g for each pair of functions. State the domain of each composite function.

f(x)=2-xg(x)=3x+1

Short Answer

Expert verified

(fog)(x)=1-3xDomain:Allrealnumbers(gof)(x)=7-3xDomain:Allrealnumbers(fof)(x)=xDomain:allrealnumbers(gog)(x)=9x+4Domain:allrealnumbers

Step by step solution

01

Given Information 

Given two functions are

f(x)=2-xg(x)=3x+1

02

Part(a): Step 1 : composition of functions

f(x)=2-xg(x)=3x+1(fog)(x)=f(g(x))=f(3x+1)=2-(3x+1)=-3x+1(fog)(x)=-3x+1

Domain is all real numbers

03

Part(b) : Step 1 : composition of functions

f(x)=2-xg(x)=3x+1(gof)(x)=g(f(x))=g(2-x)=3(2-x)+1=7-3x(gof)(x)=7-3xDomain:Allrealnumbers

04

Part(c): Step 1: composition of functions

f(x)=2-xg(x)=3x+1(fof)(x)=f(f(x))=f(2-x)=2-(2-x)=+x(fof)(x)=xDomain:Allrealnumbers

05

Part(d): Step 1: composition of functions

f(x)=2-xg(x)=3x+1(gog)(x)=g(g(x))=g(3x+1)=3(3x+1)+1=9x+4(gog)(x)=9x+4domain:Allrealnumbers

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