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$\{x \in R : 3k \leq x < 3k + 1, k \in Z\}$
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Similar Questions
If $f: R \rightarrow R$ is defined by $f(x)=x-[x]-\frac{1}{2}$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then $\{x \in R: f(x)=\frac{1}{2}\}$ is equal to :
If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} 2x & : x > 3 \\ x^2 & : 1 < x \leq 3 \\ 3x & : x \leq 1 \end{cases}$,then the value of $f(-1) + f(2) + f(4)$ is:
Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$. Then the total number of one-one maps $f: A \rightarrow B$,such that $f(1)+f(3)=14$,is:
DifficultJEE MAIN 2024
View SolutionFind the number of all one-one functions from set $A = \{1, 2, 3\}$ to itself.
Medium
View Solution$f(x)=\frac{x}{e^x-1}+\frac{x}{2}+2 \cos ^3 \frac{x}{2}$ on $R-\{0\}$ is
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