Question

Identify the function based on the description.

1. It is periodic with period $\pi$

2. If $x_1>x_2,f\left(x_1\right)>f\left(x_2\right)$ where $xϵ(-\frac{\pi }{2},\frac{\pi }{2})$

3. Domain of the function is

R - $\left\{\right(2n+1\left)\frac{\pi }{2}\right\}$ where $nϵI$

4. Range of the function is R

• A.
• B.
• C.
• D.
• E.

Answer 1

The correct option is B

Statement 1: It is given that function F(x) is a periodic function with period $\pi$

$tanx\&cotx$ are the only trigonometric functions that have period $\pi$.

Statement 2: Function f(x) is strictly increasing in the interval of $-\left(\frac{\pi }{2}\right)to\left(\frac{\pi }{2}\right)$. Tanx increases in the $-\left(\frac{\pi }{2}\right)to\left(\frac{\pi }{2}\right)$ while cotx decreases.

So, f(x) should be tanx.

This can also be confirmed by statement 3 and statement 4.

Domain of $tanx=R-\left\{\right(2n+1\left)\frac{\pi }{2}\right\}nϵI$

and Range of tanx= R

Graph of tanx is