Question

State the domain and range for the function. f(x)=3 cot (2x)

Answer 1

Answer: Domain =  $(\infty,-\infty)$.

Range = [-3,3] .

Step-by-step explanation:

The given function :  $f(x) = 3\cot (2x)$

Parent function to this function, $g(x)= \cos x$ which is a trigonometric function.

The property of this function is :

• x can take any value , so Domain of this function is $(\infty,-\infty)$.
• Also, $-1\leq\cos x\leq1$, so Range of this function is $[-1,1]$.

Now , for the given function,

Domain would be same as g(x),i.e. Domain of f(x) is $(\infty,-\infty)$.

Also,  $-1\leq\cos x\leq1\Rightarrow\ -3\leq3\cos x\leq3$

So , Range of f(x) is [-3,3]

Hence,  the domain and range for the function$f(x) = 3\cot (2x)$ is

Domain =  $(\infty,-\infty)$.

Range = [-3,3] .