Question

identify the function based on the description.

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

2. Domain of the function is $R-n\pi$ 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 a periodic 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 the 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) increase 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 cosecx is