   Chapter 2.2, Problem 22E

Chapter
Section
Textbook Problem

In Exercises 19-24, find the functions f + g, f – g, fg, and f g .22. f(x) = 1 x 2 + 1 ; g(x) = 1 x 2 − 1

To determine

To evaluate: The functions f+g,fg,fg and fg for the given function f and g .

Explanation

Given:

The given functions are f(x)=1x2+1 and g(x)=1x21 .

Calculation:

If there are two functions f and g with domain A and B then according to the algebra of functions the sum of f and g is found by the rule,

(f+g)(x)=f(x)+g(x)

Use the above definition and calculate sum of functions f and g .

(f+g)(x)=1x2+1+1x21(f+g)(x)=(x21)+(x2+1)(x2+1)(x21)=2x2x41((ab)(a+b)=a2b2)

Thus, the sum of given functions f+g is 2x2x41 .

According to the algebra of functions the difference of f and g are found by the rule,

(fg)(x)=f(x)g(x)

The difference of the functions is,

(fg)(x)==x21(x2+1)(x2+1)(x21)=x21x21(x2+1)(x21)((ab)(a+b)=a2+b2)=2x41

Thus, the difference of function fg is 2x41

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