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Question

Identify the function based on the description.

1. It is periodic with period π

2. If x1>x2,f(x1)>f(x2) where x ϵ (π2,π2)

3. Domain of the function is

R - {(2n+1)π2} where n ϵ I

4. Range of the function is R



Your Answer
A

Correct Answer
B

Your Answer
C

Your Answer
D

Your Answer
E


Solution

The correct option is B


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

tanx & cotx are the only trigonometric functions that have period π.

Statement 2: Function f(x) is strictly increasing in the interval of (π2) to (π2). Tanx increases in the (π2) to (π2) while cotx decreases.

So, f(x) should be tanx.

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

Domain of  tan x=R{(2n+1)π2} n ϵ I

and Range of tanx= R

Graph of tanx is

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