The domain of the function f(x) = sqrt{log fr | vedclass

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(B) For the function $f(x) = \sqrt{\log \frac{1}{|\sin x|}}$ to be defined,the expression inside the square root must be non-negative:$\log \frac{1}{|

Vedclass · Accepted Answer

$R - \{ n\pi, n \in I \}$

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(B) For the function $f(x) = \sqrt{\log \frac{1}{|\sin x|}}$ to be defined,the expression inside the square root must be non-negative:$\log \frac{1}{|\sin x|} \ge 0$Since $\log_a x \ge 0$ implies $x \ge 1$ (for base $10$ or $e$),we have:$\frac{1}{|\sin x|} \ge 1$$1 \ge |\sin x|$This inequality is always true for all $x$ where $\sin x$ is defined,provided $|\sin x| 
eq 0$.Since $\sin x = 0$ at $x = n\pi$ for $n \in I$,the term $\frac{1}{|\sin x|}$ becomes undefined at these points.Therefore,the domain is all real numbers except where $\sin x = 0$.Domain $= R - \{ n\pi, n \in I \}$.

The domain of the function $f(x) = \sqrt{\log \frac{1}{|\sin x|}}$ is

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