Question

Identify the function based on the description.

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

2.Domain of the function is R and the range is [-1, 1]

3.F(x) decreases strictly from 1 to -1 as x increases from 0 to $\pi$. [For eg. If $x_2>x_1,F\left(x_1\right)>f\left(x_2\right),xϵ[0,\pi ]$

4.F(x) increases strictly from -1 to 1 as x increases from $\pi to2\pi$. (foreg. If $x_2>x_1,f\left(x_2\right)>f\left(x_1\right),xϵ[\pi ,2\pi ]$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Statement 1. It is a periodic function with period $2\pi$. So, the given function can be sinx,cosx,secx or cosec x.

Statement 2. Domain of function is R. So, it can't be secx and cosecx.

Range of function lies between [-1,1]

So, given function is either sinx or cosx

Statement 3: f(x) decreases strictly from 1 to -1 as x increases from 0 to $\pi$.

f(0)=1

f$\left(\pi \right)$=-1

We, also know sin 0=0 $\&$ sin $\pi$=0

cos 0=1 $\&$ cos $\pi$=-1

Given function should be F(x)=cosx

Statement 4: f(x) increases strictly from -1 to 1 as x increases from $\pi$ to $2\pi$

Graph of f(x)=cos x is

Statement 4 also confirmed our conclusion.

Given function is F(x)=cos x