Suppose $f(x) = {(x + 1)^2}$ for $x \ge - 1$. If $g(x)$ is the function whose graph is the reflection of the graph of $f(x)$ with respect to the line $y = x$, then $g(x)$ equals

If $f(x) = \log \left[ {\frac{{1 + x}}{{1 - x}}} \right]$, then $f\left[ {\frac{{2x}}{{1 + {x^2}}}} \right]$ is equal to

Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a function which satisfies $\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y}) \forall \mathrm{x}, \mathrm{y} \in \mathrm{R} .$ If $\mathrm{f}(1)=2$ and $g(n)=\sum \limits_{k=1}^{(n-1)} f(k), n \in N$ then the value of $n,$ for which $\mathrm{g}(\mathrm{n})=20,$ is 

Which pair $(s)$ of function $(s)$ is/are equal ?

where $\{x\}$ and $[x]$ denotes the fractional part $\&$ integral part functions.

Let $f(x) = cos(\sqrt P \,x),$ where $P = [\lambda], ([.]$ is $G.I.F.)$ If the period of $f(x)$ is $\pi$. then

Domain of $f (x)$ = $\sqrt {{{\log }_2}\left( {\frac{{10x - 4}}{{4 - {x^2}}}} \right) - 1} $ , is