Question

Domain of the function $f (x) = \log_x \; \cos \; x$, is

• A. \left( - \frac{\pi}{2} , \frac{\pi}{2}\right) - \left\\{1\right\\}
• B. \left[ - \frac{\pi}{2} , \frac{\pi}{2}\right] - \left\\{1\right\\}
• C. $\left( - \frac{\pi}{2} , \frac{\pi}{2}\right)$
• D. $None\, of\, these$

Answer 1

Answer: (D)

$None\, of\, these$

Answer 2

We have the function $f(x)=\log _{x} \cos x$ $f(x)$ is defined for $\cos x>0$, $x >0, x \neq 1$ $\because \cos x >0$ $\Rightarrow -\frac{\pi}{2} < x < \frac{\pi}{2}$ Also, $x > 0, x \neq 1$ $\therefore$ Domain of $f$ is $\left(0, \frac{\pi}{2}\right)-\\{1\\}$.