The function $f(x) = x^{2} + bx + c$, where $b$ and $c$ are real constants, describes:

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be the functions defined by $f(x) = \frac{x}{1+x^2}$ and $g(x) = \frac{x^2}{1+x^2}$. Then, the correct statement$(s)$ among the following is/are:

If a set $A$ has $m$ elements and the set $B$ has $n$ elements,then the number of injections from $A$ to $B$ is

If $f: N \times N \rightarrow N$ is defined by $f(m, n) = 2^{m-1}(2n-1)$ for all $(m, n) \in N \times N$,then $f$ is

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 $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x + 2, & x \leq -1 \\ x^2, & -1 < x < 1 \\ 2 - x, & x \geq 1 \end{cases}$. Then the value of $f(-1.75) + f(0.5) + f(1.5)$ is