Question

Identify the function based on the description.

1. It is periodic with period $2\pi$

2. Domain of the function is $R-\left[n\pi \right]$ where $nϵz$

3. Range of the function is R-(-1,1)

4.The graphs of F(x) tends to meet y-axis at $\infty$ at $x=0,\pm \pi ,\pm 2\pi ,......$

5. If $x_2>x_1$ then $F\left(x_2\right)>F\left(x_1\right)$ when $xϵ[\frac{\pi }{2},\pi )$

6.If $x_2>x_1$ then $F\left(x_1\right)>F\left(x_2\right)$ when $xϵ(0,\frac{\pi }{2}]$

• A.
• B.
• C.
• D.
• E.

Answer 1

The correct option is C

Statement 1. It is aperiodic function with period $2\pi$. So, given function can be sinx,cosx,

secx or cosec x.

Statement 2. Domain of the function is $R-n\pi$ and Range of function is R-(-1,1)

Domain $\&$ Range of sin x $\&$ cosx is R $\&$ [-1,1] respectively

F(x) should be either secx or cosec x

F(x) increases in the interval of $[\frac{\pi }{2},\pi )$ and it decreases in the interval of $(0,\frac{\pi }{2}]$

Based on the given information we can definitely say f(x) is a cosecx function.

It also tends to meet y-axis at $\infty$ at $x=0\pm \pi ,\pm 2\pi ..........$

Graph of cosex is