$f : R \to R$ is defined as

$f(x) = \left\{ {\begin{array}{*{20}{c}}
{{x^2} + 2mx – 1\,,}&{x \leq 0}\\
{mx – 1\,\,\,\,\,\,\,\,\,\,\,\,\,,}&{x > 0}
\end{array}} \right.$

 If $f (x)$ is one-one then the set of values of $'m'$ is

Let for $a \ne {a_1} \ne 0,$ $f\left( x \right) = a{x^2} + bx + c\;,g\left( x \right) = {a_1}{x^2} + {b_1}x + {c_1},p\left( x \right) = f\left( x \right) – g\left( x \right),$ If $p\left( x \right) = 0$ only for  $ x=-1 $ and $p\left( { – 2} \right) = 2$ then value of $p\left( 2 \right)$ is

If $f(x)$ satisfies the relation $f\left( {\frac{{5x – 3y}}{2}} \right)\, = \,\frac{{5f(x) – 3f(y)}}{2}\,\forall x,y\in R$ $f(0) = 1, f '(0) = 2$ then period of $sin \ (f(x))$ is

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

Function $f(x)={\left( {1 + \frac{1}{x}} \right)^x}$ then Domain of $f (x)$ is