Question

Given the graph of the function $y=-2\tan \left(3x\right),\forall x\in R$
Choose the correct options.

Answer 1

Given the graph of $y=-2\tan \left(3x\right)\forall x\in R$

We observe from the graph that the period of $y=-2\tan 3x\text{is}\frac{\pi }{3}.$

Since we know that $\tan x$ is defined for $x\ne (2n+1)\frac{\pi }{2}\forall x\in Z.$
Therfore $-2\tan 3x$ will be defined for $3x\ne (2n+1)\frac{\pi }{2},\forall x\in Z.$
$\Rightarrow x\ne (2n+1)\frac{\pi }{6},\forall x\in Z.$
Therfore the Domain of $y=-2\tan 3x$ is $R-\left\{\right(2n+1\left)\frac{\pi }{6}\right\}\forall n\in Z.$