Precalculus

9th Edition

ISBN: 9780321716835

Author: Michael Sullivan

Publisher: Addison Wesley

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Question

Chapter 10, Problem 10CR

To determine

The domain of the function $f(x)=3sinx+cosx$

Expert Solution & Answer

Answer to Problem 10CR

Solution:

The domain of $f(x)=3sinx+cosx$ is ${x|x≠3π4+πn ; n∈ℤ}$

Explanation of Solution

Given information:

The function $f(x)=3sinx+cosx$

Explanation:

Consider the function $f(x)=3sinx+cosx$

Domain is the set of input values at which the function is defined.

The given function is a rational function which is not defined when the denominator becomes zero.

That is, the function is not defined, when $sinx+cosx=0$

Consider $sinx+cosx=0$

Divide both sides by $cosx$

$sinxcosx+cosxcosx=0cosx$

$⇒tanx+1=0$

$⇒tanx=− 1$

$⇒x=3π4+πn ; n$ is an integer

Therefore, the domain of $f(x)=3sinx+cosx$ is ${x|x≠3π4+πn ; n∈ℤ}$

Chapter 10, Problem 9CR

Chapter 10, Problem 11CR

Chapter 10 Solutions

Precalculus

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The domain of the function f ( x ) = 3 sin x + cos x

Solution Summary: The author explains that the given function is a rational function which is not defined when the denominator becomes zero.

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The domain of the function $f(x)=3sinx+cosx$

Answer to Problem 10CR

Explanation of Solution

Chapter 10 Solutions

Additional Math Textbook Solutions

The domain of the function f ( x ) = 3 sin x + cos x

Solution Summary: The author explains that the given function is a rational function which is not defined when the denominator becomes zero.

Videos

The domain of the function f(x)=3sinx+cosx<m:math><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow><m:mo>=</m:mo><m:mfrac><m:mn>3</m:mn><m:mrow><m:mi>sin</m:mi><m:mi>x</m:mi><m:mo>+</m:mo><m:mi>cos</m:mi><m:mi>x</m:mi></m:mrow></m:mfrac></m:mrow></m:math>

Answer to Problem 10CR

Explanation of Solution

Chapter 10 Solutions

Additional Math Textbook Solutions

The domain of the function $f(x)=3sinx+cosx$