Functions Test ...

If $$f:R\rightarrow R\quad defined\quad by\quad f\left( x \right) =\frac { { e }^{ { x }^{ 2 } }-{ e }^{ { -x }^{ 2 } } }{ { e }^{ x^{ 2 } }+{ e }^{ { -x }^{ 2 } } } ,\quad then\quad f\quad is$$

If $$y^2 = ax^2 +bx+c$$, then $$y^2 \dfrac{d^2y}{dx^2}$$ is

The domain of definition of the function $$f(x)=\sqrt{log_{x^2-1}x}$$ is-

If $$\left|x\right|$$ denotes the integral part of $$x$$ and $$f(x)$$ has domain $$\left[ -\dfrac { 5 }{ 2 } ,2 \right] $$, the domain of $$f\left( \left[ \left| x \right|  \right]  \right) $$ is

The domain of the real valued function $$f(x)$$ for which $$4^{f(x)+4^{1-f(x)}}= 4^{x}$$ is 

The domain of the function $$f(x) =\log_{\left[x+\dfrac{1}{2}\right]} |x^{2}-5x+6|$$ is 

The function $$f:R\rightarrow R$$ defined by $$f\left(x\right)=6^ {x}+6$$ is

$$f(x)$$ is

If $$fxln\left(1+\dfrac{1}{x}\right)dx=p(x)ln\left(1+\dfrac{1}{x}\right)+\dfrac{1}{2}x-\dfrac{1}{2}ln(1+x)+c$$, being arbitary costant, then

The domain of $$\frac{x+1}{\sqrt{x^{2}-5x+6}}$$ is