Relations and F...

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 $$f(x)=\frac { \alpha x }{ x+1 } $$, where $$x\neq -1$$ and (fof) (x) = x, then $$\alpha =$$

Let $$f:R\rightarrow R$$ be defined as 
$$f(x)={ x }^{ 3 }+{ 2x }^{ 2 }+4x+sin\left( \dfrac { \pi x }{ 2 }  \right) $$ and  $$g(x)$$be the inverse function of f(x), then $${ g }^{ ' }(8)$$is equal to :

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

Let n(A) = 4 and n(B) = 6. Then the number of one - one  functions from A to B is 

$$f(x)$$ is

let $$f:R\rightarrow R$$ be a function defined by $$f(x)=\frac { { x }^{ 2 }-3x+4 }{ { x }^{ 2 }+3x+4 }$$ then f is

A number of decimal system when represented in binary system then its first and last digits are same and the rest digits are also of another kind. Further this number appears to be palindrome of number. The number is

If $$f:Z\rightarrow Z, f(n)=\begin{cases} n+1;\quad n\quad is\quad even \\ n-3;\quad n\quad is\quad odd \end{cases}$$ is $$ f$$ is ...........

Which one of the following functions is not invertible?