Question

The domain and range of $\tan x$ and $3\tan x$ are the same.

• A. False
  
• B. True

Answer 1

The correct option is B True

Domain of $\tan x=R-(2n+1)\frac{\pi }{2}$, $x\in R$.

Notice that the domain of $y=3\tan x$ is the same as the domain for $y=\tan \left(x\right)$ because the graph was stretched vertically when a constant greater that 1 was multiplied with it, which does not change where the vertical asymptotes occur.

As the range of $y=\tan x$ is the set of all real numbers, on multiplying it by $3$, the range will remain the same.
$\Rightarrow$ range $\in (-\infty ,\infty )$