Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The range of the function $f(x)=\sin[x],-\frac{π}{4}<x<\frac{π}{4}$, where [x] denotes the greatest integer ≤ x is

Options:

{0}

{0, -1}

$\{0, ±\sin 1\}$

$\{0, -\sin 1\}$

Correct Answer:

$\{0, -\sin 1\}$

Explanation:

When $-\frac{π}{4}<x<0⇒-1<-\frac{π}{4}<x⇒[x]=-1$

$⇒y=\sin(-1)=-\sin 1$, when $0≤x<\frac{π}{4}<1⇒[x]=0$

$y=\sin 0=0$