Question

For the given graph of $y=2\cot (x+\pi /4);y\in R$. Select the correct statements.

• A. Domain: $R-(4n-1)\pi /2;n\in Z$
• B. $\text{For}x\in [-\pi ,3\pi ],y=0$ at $x=-3\pi /4,\pi /4,5\pi /4,9\pi /4$
• C. $\text{For}x\in [-\pi ,3\pi ],y=0$ at $x=-3\pi /2,\pi /2,5\pi /4,9\pi /4$
• D. Domain: $R-(4n-1)\pi /4;n\in Z$

Answer 1

Answer: (B), (D)

Domain: $R-(4n-1)\pi /4;n\in Z$

Given the graph of $\cot x$


Here, $\cot x$ is not defined for $x=-\pi /4,3\pi /4,7\pi /4...$
Or Domain(D): $R-(4n-1)\pi /4$
Also, For $x\in [-\pi ,3\pi ],y=0$ at points:
$x=-3\pi /4,\pi /4,5\pi /4,9\pi /4$