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

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

The function $f: R \rightarrow R$ is defined by $f(x)=3^{-x}$. Observe the following statements about it:
$I$. $f$ is one-one
$II$. $f$ is onto
$III$. $f$ is a decreasing function
Out of these, the true statements are:

Let $R$ be the set of all real numbers. Statement $I$: The function $f: \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow R$ defined by $f(x) = \sec x + \tan x$ is a one-one function. Statement $II$: The function $f: [0, \infty) \rightarrow R$ defined by $f(x) = x^2$ is a one-one function. Which of the above statements is(are) true?

If $f: R \rightarrow R$ is defined by $f(x) = x^2 + 3x + 4$,then the function $f$ 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