$f(x) = \log \left( \left( \frac{2x^2 - 3}{x} \right) + \sqrt{\frac{4x^4 - 11x^2 + 9}{|x|}} \right)$ 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.

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 $f : R \to R$ be defined as $f(x) = e^{x^2} + \cos x$. Then $f$ is:

The function $f(x) = \sin (\log (x + \sqrt {x^2 + 1}))$ is

If the function $f: R \rightarrow R$ is defined by $f(x) = |x|(x - \sin x)$,then which of the following statements is $TRUE$?