The function $f: R-\{1\} \rightarrow R-\{4\}$ defined by $f(x) = \frac{4x-3}{x-1}$ for $x \in R-\{1\}$ is

If the function $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} 2x-3, & \text{if } x < -2 \\ x^2-1, & \text{if } -2 \leq x \leq 2 \\ 3x+2, & \text{if } x > 2 \end{cases}$ then $f$ is

$A$ function $f: R \rightarrow R$ defined by $f(x) = \begin{cases} 2x+3, & x \leq \frac{4}{3} \\ -3x^2+8x, & x > \frac{4}{3} \end{cases}$ is

If $f: N \rightarrow Z$ is defined by $f(n)=\begin{cases} 2 & \text{if } n=3k, k \in Z \\ 10 & \text{if } n=3k+1, k \in Z \\ 0 & \text{if } n=3k+2, k \in Z \end{cases}$, then $\{n \in N: f(n)>2\}$ is equal to

Let $A = \{x_1, x_2, x_3, \dots, x_7\}$ and $B = \{y_1, y_2, y_3\}$ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f: A \to B$ which are onto,if there exist exactly three elements $x$ in $A$ such that $f(x) = y_2$,is equal to

The number of onto functions $f$ from $\{1, 2, 3, \dots, 20\}$ to $\{1, 2, 3, \dots, 20\}$ such that $f(k)$ is a multiple of $3$ whenever $k$ is a multiple of $4$ is: