If $R$ denotes the set of all real numbers,then the function $f: R \to R$ defined by $f(x) = [x]$ is:

The function $f: R \rightarrow R$ defined by $f(x) = e^x + e^{-x}$ is

The real-valued function $f: R \rightarrow [ \frac{5}{2}, \infty )$ defined by $f(x) = | 2x + 1 | + | x - 2 |$ is

Let a function $f: N \rightarrow N$ be defined by
$f(n) = \begin{cases} 2n, & n = 2, 4, 6, 8, \dots \\ n-1, & n = 3, 7, 11, 15, \dots \\ \frac{n+1}{2}, & n = 1, 5, 9, 13, \dots \end{cases}$
Then,$f$ is

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

If $f(x) = \sin([\pi^2]x) - \sin([-\pi^2]x)$,where $[x]$ denotes the greatest integer function $\leq x$,then which of the following is not true?