Functions Test ...

Difference between the greatest and the least values of the function
$$f(x) = x(ln x - 2)$$ on $$[1, e^{2}]$$ is

The function $$f :\left[-\dfrac{1}{2}, \dfrac{1}{2}\right]\rightarrow \left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$$ defined by $$f(x)=\sin^{-1}(3x-4x^{3})$$ is 

The value of the function f(x)=$$\dfrac { { x }^{ 2 }-3x+2 }{ { x }^{ 2 }+x-6 } $$ lies in the interval:

The domain of $$f(x)=\log(||x-2|-2|-1)$$ is$$

Let g be the inverse function of differentiable function f and $$G\left( x \right) =\frac { 1 }{ g\left( x \right)  } if\quad f\left( 4=2 \right) $$ and $$f'\left( 4 \right) =\frac { 1 }{ 16 } $$, then the value of $${ \left( G'\left( 2 \right)  \right)  }^{ 2 }$$ equals to:

If $$f:( - 1,1) \to B$$ , is a function defined by $$f(x) = {\tan ^{ - 1}}\dfrac{{2x}}{{1 - {x^2}}}$$, then find $$B$$ when $$f(x)$$ is both one-one and onto function. 

If  $$f \left( \dfrac { x + y } { 2 } \right) = \dfrac { f ( x ) + f ( y ) } { 2 }$$  for all  $$x , y \in R$$  and  $$f ^ { \prime } ( o ) = - 1 , f ( o ) = 1$$  then  $$f(2)=$$

If $$f(x)=\dfrac {4^{x}}{4^{x}+2}$$, then the value of $$f(x)+f(1-x)$$ is

Let $$f(x)$$ be a function whose domain is $$[-5,7]$$. Let $$g(x) =|2x+5|$$, then domain of $$(fog) (x)$$ is 

If $$f(x)=x^{3}+x^{2}f'(1)+xf''(2)+f'''(3)\ \forall x\ \epsilon \ R$$, then $$f(x)$$ is