Let $[\cdot]$ denote the greatest integer function. If $f(x) = [x]$ and $g(x) = 3[\frac{x}{3}]$,then the set of all real $x$ such that $f(x) = g(x)$ is
- A$R$
- B$\{x \in R : x = 3k, k \in Z\}$
- C$\{x \in R : 3k - 1 < x \leq 3k, k \in Z\}$
- D$\{x \in R : 3k \leq x < 3k + 1, k \in Z\}$
Explore More
Similar Questions
$f:[-2,2] \rightarrow[-2,2]$ and $g:[-2,2] \rightarrow[0,4]$ are two functions defined as $f(x)=\begin{cases} -2, & -2 \leq x \leq 0 \\ x^2-2, & 0 \leq x \leq 2 \end{cases}$ and $g(x)=|f(x)|+f(|x|)$,then
If $f(x) = \sin([\pi^2]x) - \sin([-\pi^2]x)$,where $[x]$ denotes the greatest integer function $\leq x$,then which of the following is not true?
MediumKCET 2025
View SolutionIf $f(x) = \begin{cases} [x], & -3 < x \leq -1 \\ |x|, & -1 < x < 1 \\ |[x]|, & 1 \leq x < 3 \end{cases}$ then the set $\{x : f(x) \geq 0\}$ is equal to
The function $f: R \rightarrow R$ defined by $f(x)=\frac{x}{\sqrt{1+x^2}}$ is
Let $A = \{x \in R : -1 \leq x \leq 1\}$ and $f: A \rightarrow A$ be a mapping defined by $f(x) = x|x|$. Then $f$ is
MediumWBJEE 2020
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo