Question

The set of all points of discontinuity of the function $f\left(x\right)=\frac{\tan x\log x}{1-\cos 4x}$ contains

• A. $\left\{\frac{n\pi }{2}:nϵI\right\}$
• B. $\left\{\frac{n\pi }{2}:nϵQ\right\}$
• C. $(-\infty ,0)\cup \left\{\frac{n\pi }{2}:nϵN\right\}$
• D. none of these

Answer 1

Answer: (A), (C)

The correct options are
A $\left\{\frac{n\pi }{2}:nϵI\right\}$
C $(-\infty ,0)\cup \left\{\frac{n\pi }{2}:nϵN\right\}$

This function is discontinuous when the denominator equals zero.
$1-\cos 4x=0\Rightarrow \cos 4x=1\Rightarrow 4x=2n\pi \Rightarrow x=\frac{n\pi }{2},nϵI$
Also, the function $\log x$is not defined for $x<0$.
So, the points of discontinuity include $(-\infty ,0)\cup \{\frac{n\pi }{2}:nϵI\}$.
So, options A and C are the right answers.