The range of the function f(x)= sin [x],- (π/4)

Question

The range of the function f(x)= sin [x],- (π/4) < x < (π/4) where [x] denotes the greatest integer ≤ x, is  (A)  0  (B)  0,-1  (C)  0, ± sin 1  (D)  0, - sin 1

Tardigrade Admin · Accepted Answer

Given, f(x)= sin [x],-(π/4)< x< (π/4) Clearly, sin 0=0 and [(π/4)]=[(3.14/4)]=0 ∴ ∀ x ∈[0, (π/4)], sin [x]=0 ∀ x ∈[-(π/4), 0),[x]=-1 ∴ sin [x]= sin (-1)=- sin 1 So, the range of f(x) is 0,- sin 1 .

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

${0}$

${0, - 1}$

${0, \pm s in 1}$

${0, - s in 1}$

Q. The range of the function f(x)=sin[x],−4π​<x<4π​ where [x] denotes the greatest integer ≤x, is ________

{0}

{0,−1}

{0,±sin1}

{0,−sin1}

Given, f(x)=sin[x],−4π​<x<4π​ Clearly, sin0=0 and [4π​]=[43.14​]=0 ∴∀x∈[0,4π​],sin[x]=0 ∀x∈[−4π​,0),[x]=−1 ∴sin[x]=sin(−1)=−sin1 So, the range of f(x) is {0,−sin1}.

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

${0}$

${0, - 1}$

${0, \pm s in 1}$

${0, - s in 1}$