Let $R = \{ a, b, c, d, e \}$ and $S = \{1, 2, 3, 4\}$. The total number of onto functions $f: R \rightarrow S$ such that $f(a) \neq 1$ is equal to $.............$.

Let $f: R \rightarrow R$ be defined by $f(x) = \left\{\begin{array}{cc} 2x, & x > 3 \\ x^2, & 1 < x \leq 3 \\ 3x, & x \leq 1 \end{array}\right.$. Then,the value of $f(-2) + f(3) + f(4)$ is:

Let a function $f: (0, \infty) \to (0, \infty)$ be defined by $f(x) = |1 - \frac{1}{x}|$. Then $f$ is

Let $f: R \rightarrow R$ be defined by $f(x)=x^{4}$,then

If a set $A$ has $n$ elements,then the number of functions defined from $A$ to $A$ that are not one-one is

Let $f : N \rightarrow N$ be defined by $f(n) = \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$ for all $n \in N$. State whether the function $f$ is bijective. Justify your answer.