Let $f: X \rightarrow X$ be such that $f(f(x)) = x$ for all $x \in X$ and $X \subseteq \mathbb{R}$. Then:

Let $f(x) = \cos(\sqrt{P}x),$ where $P = [\lambda]$ and $[.]$ denotes the Greatest Integer Function. If the period of $f(x)$ is $\pi$,then:

Given that for any $n \in N$,there exist an odd integer $q$ and a non-negative integer $r$ such that $n$ can be written uniquely as $n = q \times 2^r$. Let $f: N \rightarrow N \times N$ be a function defined by $f(n) = \left(r+1, \frac{q+1}{2}\right)$. Then,

$f: X \rightarrow R$,where $X = \{x \mid 0 < x < 1\}$,is defined as $f(x) = \frac{2x-1}{1-|2x-1|}$. Then:

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

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