The number of functions $f: \{1, 2, 3, 4\} \to \{a, b, c\}$, which are not onto, is:

Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} 2x; & x > 3 \\ x^2; & 1 < x \leq 3 \\ 3x; & x \leq 1 \end{cases}$. Then $f(-1) + f(2) + f(4)$ is

Let $A = \{1, 2, 3, 4, 5, 6\}$. The number of functions $f: A \to A$ such that $f(m) + f(n) = 7$ whenever $m + n = 7$ is:

Given that $f: S \rightarrow R$ is said to have a fixed point at $c \in S$ if $f(c)=c$. Let $f:[1, \infty) \rightarrow R$ be defined by $f(x)=1+\sqrt{x}$. Then:

Check the injectivity and surjectivity of the function $f: R \rightarrow R$ defined by $f(x) = x^2$.

Let $f: R \rightarrow R$ be defined as $f(x)=3x$. Choose the correct answer.