(D) Given the function $f(x) = \sin [x]$ for $-\frac{\pi}{4} < x < \frac{\pi}{4}$. We know that $\frac{\pi}{4} \approx 0.785$ and $-\frac{\pi}{4} \app

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) Given the function $f(x) = \sin [x]$ for $-\frac{\pi}{4} We know that $\frac{\pi}{4} \approx 0.785$ and $-\frac{\pi}{4} \approx -0.785$. The interval for $x$ is $(-0.785, 0.785)$. For $x \in [0, 0.785)$,the greatest integer value $[x] = 0$. Thus,$f(x) = \sin(0) = 0$. For $x \in (-0.785, 0)$,the greatest integer value $[x] = -1$. Thus,$f(x) = \sin(-1) = -\sin(1)$. Therefore,the range of the function is $\{0, -\sin 1\}$.

Class 12 Mathematics Relation and Function Domain and Range

Easy

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

KCET 2013 All KCET

A
$\{0\}$
B
$\{0, -1\}$
C
$\{0, \pm \sin 1\}$
D
$\{0, -\sin 1\}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Relation and Function

Subtopic

Domain and Range

Previous Year

KCET 2013 Paper All KCET years →

Range of the function $f(x) = \sin^2(x^4) + \cos^2(x^4)$ is

Medium

View Solution

Let the domain of the function $f(x) = \log_3 \log_5 (7 - \log_2 (x^2 - 10 x + 85)) + \sin^{-1} ( | \frac{3 x - 7}{17 - x} | )$ be $(\alpha, \beta]$. Then $\alpha + \beta$ is equal to :

DifficultJEE MAIN 2026

View Solution

Let $\rho$ be a relation defined on the set of natural numbers $N$, as $\rho = \{(x, y) \in N \times N: 2x + y = 41\}$. Then the domain $A$ and range $B$ are:

EasyWBJEE 2023

View Solution

Let $y = \sqrt{\frac{(x + 1)(x - 3)}{(x - 2)}}$. Then,the set of all real values of $x$ for which $y$ takes real values is:

DifficultIIT 1980

View Solution

The domain and range of $f(x) = \frac{1}{\sqrt{|x| - x^2}}$ are $A$ and $B$ respectively. Then $A \cup B =$

MediumTS EAMCET 2025

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

Range of the function $f(x) = \sin^2(x^4) + \cos^2(x^4)$ is

Let the domain of the function $f(x) = \log_3 \log_5 (7 - \log_2 (x^2 - 10 x + 85)) + \sin^{-1} ( | \frac{3 x - 7}{17 - x} | )$ be $(\alpha, \beta]$. Then $\alpha + \beta$ is equal to :

Let $\rho$ be a relation defined on the set of natural numbers $N$, as $\rho = \{(x, y) \in N \times N: 2x + y = 41\}$. Then the domain $A$ and range $B$ are:

Let $y = \sqrt{\frac{(x + 1)(x - 3)}{(x - 2)}}$. Then,the set of all real values of $x$ for which $y$ takes real values is:

The domain and range of $f(x) = \frac{1}{\sqrt{|x| - x^2}}$ are $A$ and $B$ respectively. Then $A \cup B =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module