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Chapter 2: Q. 13 (page 124)

Find f+g,f-g,f鈰�gand fgfor each pair of functions. State the domain of each of these functions.

f(x)=3x2+x+1g(x)=3x

Short Answer

Expert verified

For f(x)=3x2+x+1;g(x)=3x, we get:

f+g=3x2+4x+1and its domain is the set of all real numbers.

f-g=3x2-2x+1and its domain is the set of all real numbers.

f鈰�g=9x3+3x2+3xand its domain is the set of all real numbers.

fg=3x2+x+13xand its domain is {x|x鈮�0}.

Step by step solution

01

Step 1. Given information

We have been given:

f(x)=3x2+x+1g(x)=3x

We have to find f+g,f-g,f鈰�gand fgfor the pair of functions and state the domain of each of these functions.

02

Step 2. Find f+g and its domain. 

We know f+g=f(x)+g(x).

Therefore,

f+g=3x2+x+1+3x=3x2+4x+1

Its domain is the set of all real numbers.

03

Step 3. Find f-g and its domain. 

We know f-g=f(x)-g(x).

Therefore,

f-g=(3x2+x+1)-(3x)=3x2+x+1-3x=3x2-2x+1

Its domain is the set of all real numbers.

04

Step 4. Find f⋅g and its domain. 

We know f鈰�g=f(x)鈰�g(x).

Therefore,

f鈰�g=(3x2+x+1)(3x)=9x3+3x2+3x

Its domain is the set of all real numbers.

05

Step 5. Find fg and its domain. 

We know fg=f(x)g(x).

Therefore,

role="math" localid="1645974118795" fg=3x2+x+13x

The domain will be the set of all real numbers except those that make the denominator zero.

3x=0x=0

The domain will be {x|x鈮�0}.

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role="math" localid="1645828501222" F(x)=2if0<x鈮�14if1<x鈮�310if3<x鈮�45int(x+1)+2if4<x<951if9鈮�x鈮�24

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