Chapter 10: Q. 10 (page 701)

What is the domain of the function $f (x) = \frac{3}{\sin x + \cos x}$

Short Answer

Expert verified

The domain of the function is $R - \{n π - \frac{π}{4}\}$

Step by step solution

Step 1. Given Information

The given function is $f (x) = \frac{3}{\sin x + \cos x}$

Step 2. Explanation

First simplify the given function,

$y = \frac{3}{\sin x + \cos x} y = \frac{3}{\sqrt{2} (\frac{1}{\sqrt{2}} \sin x + \frac{1}{\sqrt{2}} \cos x)} y = \frac{3}{\sqrt{2} \sin (x + \frac{π}{4})}$

The obtained function is not defined when the value sine function drops to zero. The function is not defined for $x = n π - \frac{π}{4}$ , where n is any integer.

Thus, the domain of the function is $R - \{n π - \frac{π}{4}\}$ where R is the set of all real numbers.

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What is the domain of the function $f (x) = \frac{3}{\sin x + \cos x}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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What is the domain of the functionf(x)=3sinx+cosx

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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What is the domain of the function $f (x) = \frac{3}{\sin x + \cos x}$