Relations and F...

if $$f\left( x \right) = 3x + 2$$ , $$g\left( x \right) = {x^2} + 1$$,then the values of $$\left( {f_og} \right)\left( {{x^2} - 1} \right)$$

Let A = {1,2,3,4,5} and B={1,2,3,4,5}. If $$f:A\rightarrow B$$ is an one-one function and $$f(x)=x$$ holds only for one value of  $$x\epsilon \{ 1,2,3,4,5\} ,$$ then the number of such possible function 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 

If $$f\left( x \right) = \frac{{x - 1}}{{x + 1}}$$, then $$f^{-1}\left( x \right)$$ 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. 

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

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

Let S be a non-empty set and P(S) be the power set of set S. Find the identity element for the union $$(\cup)$$ as a binary operation on $$P(S)$$.

If $$\begin{bmatrix} \sin { \left( \dfrac { \pi  }{ 2 }  \right)  }  & \cos { \left( \dfrac { \pi  }{ 3 }  \right)  }  \\ 2\tan { \left( \dfrac { \pi  }{ 4 }  \right)  }  & 2k \end{bmatrix}$$ is not invertible, then $$k=$$