Algebra 2

1st Edition

ISBN: 9780078884825

Author: McGraw-Hill/Glencoe

Publisher: Glencoe/McGraw-Hill School Pub Co

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Question

Chapter EP, Problem 7.1.4EP

To determine

To calculate: The value of $(f+g)(x),(f−g)(x),(f⋅g)(x), and (fg)(x)$ where $f(x)=x2+1 and g(x)=x+1$ .

Expert Solution & Answer

Answer to Problem 7.1.4EP

The value of

$(f+g)(x)=x2+x+2,(f−g)(x)=x2−x,(f⋅g)(x)=x3+x2+x+1, and (fg)(x)=x2+1x+1$ , $x≠−1$ .

Explanation of Solution

Given information:

The functions $f(x)=x2+1 and g(x)=x+1$ .

Formula used:

The sum of two functions $f(x)and g(x)$ is $(f+g)(x)=f(x)+g(x)$ .

The difference of two functions $f(x)and g(x)$ is $(f−g)(x)=f(x)−g(x)$ .

The product of two functions $f(x)and g(x)$ is $(f⋅g)(x)=f(x)⋅g(x)$ .

The quotient of two functions $f(x)and g(x)$ is $(fg)(x)=f(x)g(x)$ .

Calculation:

Consider the functions $f(x)=x2+1 and g(x)=x+1$ .

Recall that sum of two functions $f(x)and g(x)$ is $(f+g)(x)=f(x)+g(x)$ .

Apply it,

$(f+g)(x)=f(x)+g(x)=x2+1+x+1=x2+x+2$

Recall that difference of two functions $f(x)and g(x)$ is $(f−g)(x)=f(x)−g(x)$ .

Apply it,

$(f−g)(x)=f(x)−g(x)=x2+1−(x+1)=x2+1−x−1=x2−x$

Recall that product of two functions $f(x)and g(x)$ is $(f⋅g)(x)=f(x)⋅g(x)$ .

Apply it,

$(f⋅g)(x)=f(x)⋅g(x)=(x2+1)(x+1)=x3+x2+x+1$

Recall that quotient of two functions $f(x)and g(x)$ is $(fg)(x)=f(x)g(x)$ .

Apply it,

$(fg)(x)=f(x)g(x)=x2+1x+1$

The domain of the above expression is defined when denominator is not equal to 0.

That is,

$x+1≠0x≠−1$

For the quotient to be defined $x≠−1$ .

Thus, the value of

$(f+g)(x)=x2+x+2,(f−g)(x)=x2−x,(f⋅g)(x)=x3+x2+x+1, and (fg)(x)=x2+1x+1$ , $x≠−1$ .

Chapter EP, Problem 7.1.3EP

Chapter EP, Problem 7.1.5EP

Chapter EP Solutions

Algebra 2

Ch. EP - Prob. 1.1.1EP Ch. EP - Prob. 1.1.2EP Ch. EP - Prob. 1.1.3EP Ch. EP - Prob. 1.1.4EP Ch. EP - Prob. 1.1.5EP Ch. EP - Prob. 1.1.6EP Ch. EP - Prob. 1.1.7EP Ch. EP - Prob. 1.1.8EP Ch. EP - Prob. 1.1.9EP Ch. EP - Prob. 1.1.10EP

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The value of ( f + g ) ( x ) , ( f − g ) ( x ) , ( f ⋅ g ) ( x ) , and ( f g ) ( x ) where f ( x ) = x 2 + 1 and g ( x ) = x + 1 .

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Answer to Problem 7.1.4EP

Explanation of Solution

Chapter EP Solutions

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