Question

Given the graph of $y=2\tan (x+\frac{\pi }{4})\forall y\in R.$
Then, select the correct statement(s).

• A. $\text{For}x\in [-2\pi ,2\pi ],y=0\text{at:}$
  $x=\frac{-5\pi }{4},\frac{-\pi }{4},\frac{3\pi }{4},\frac{7\pi }{4}$
• B. Domain: $R-(8n+1)\pi /4;n\in Z$
• C. Domain: $R-(4n+1)\pi /4;n\in Z$
• D. $\text{For}x\in [-2\pi ,2\pi ],y=0\text{at:}$
  $x=\frac{-5\pi }{4},\frac{-\pi }{4},\frac{3\pi }{4},\frac{5\pi }{4}$

Answer 1

Answer: (A), (C)

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

Given the graph of $y=2\tan (x+\frac{\pi }{4})\forall y\in R$


Now, as per the graph, the function is not defined for values:
$\frac{-7\pi }{4};\frac{-3\pi }{4};\frac{\pi }{4};\frac{5\pi }{4};\frac{9\pi }{4}$

Mathematically written as:
$R-(4n+1)\pi /4\forall n\in Z$

For $x\in [-2\pi ,2\pi ],y=0$ at points:

$x=\frac{-5\pi }{4},\frac{-\pi }{4},\frac{3\pi }{4},\frac{7\pi }{4}$