Find the domain of the function f ( x ) = 1 x + 1 x + 1 + 1 x + 2

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 19RE
To determine

Find the domain of the function f(x)=1x+1x+1+1x+2

Expert Solution

The domain of the function f(x)=1x+1x+1+1x+2 is [(,2)(2,1)(1,0)(0,)]

Explanation of Solution

Given information: Consider the function f(x)=1x+1x+1+1x+2

Calculation:

A rational expression is not defined when the denominator is 0.

Since, A rational expression is not defined when the denominator is 0.

Since

(i)x0

Hence the given function is defined for all the values of x in the set of real numbers except of the value x=0 .

(ii)x+10x1

Hence the given function is defined for all the values of x in the set of real numbers except of the value x=1 .

(iii)x+20x2

Hence the given function is defined for all the values of x in the set of real numbers except of the value x=2 .

Thus, the domain of the function f(x)=1x+1x+1+1x+2 is [(,2)(2,1)(1,0)(0,)]

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