Question

If $\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\left[(\mathrm{x}-1){\cos }^{-1}(2\mathrm{x}+1)\tan 3\mathrm{x}\right]}$ then, $D\_\left\{f\right\}$ is

• A. $\left\{-1,0,1\right\}$
• B. {n$\pi$ : n∈ I}
• C. {n$\pi$ : n ∈ I}
• D. None of these

Answer 1

The correct option is D

None of these

Explanation for the incorrect option

option(A):

$\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\left[(\mathrm{x}-1){\cos }^{-1}(2\mathrm{x}+1)\tan 3\mathrm{x}\right]}$

The function $f\left(x\right)$ is not defined if

Therefore, Option (A) is wrong.

Option(B) and option (c):

$$\begin{gathered} \left|\mathrm{x}\right|-1=0 \\ \mathrm{x}=\pm 1 \\ \tan 3\mathrm{x}=0 \\ \mathrm{x}=\mathrm{n\pi }\mathrm{and}\frac{\mathrm{n\pi }}{3} \end{gathered}$$

Therefore, option (B) and option (c) are wrong.

Hence, the correct option is an option (D).