The range of the function $f(x)=\sin[x],

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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