Relations and F...

If $$f(x)=\frac{x}{\sqrt{1-x^{2}}}$$ and g(x) = $$f(x)=\frac{x}{\sqrt{1+x^{2}}}$$ , then (fog)(x) =

If $$ f ( x ) = \left( a - x ^ { n } \right) ^ { 1 / n }$$ where $$ a > 0$$ and } $$n$$ is a positive integer then$$( f o f ) ( x )$$ is

if $$f\left( x \right) = \log \left( {\dfrac{{1 +x}}{{1 - x}}} \right)$$ and $$g\left( x \right) = \dfrac{{3x + {x^3}}}{{1 + 3{x^2}}}$$ then $$\left( {f(g(x)))} \right)$$ is equal to

Let $$f:R\rightarrow R$$ is a function satisfying $$f(2-x)=f(2+x)$$ and $$f(20-x)=f(x)\forall x\in R$$
If $$f(0)=5$$ then the minimum possible no. of values of $$x$$ satisfying $$f(x)=5$$ for $$x=[0.,70]$$, is

Let $$f\left( x \right) = {x^2}$$ and $$g\left( x \right) = {2^x}$$. Then the solution of the equation $$fog\left( x \right) = gof\left( x \right)$$ is

All values of a for which f : R $$ \to R$$ defined by f(x)= $${x^3} + a{x^2} + 3x + 100$$ is a one one functions, are

If $$f ( x ) = \left( a - x ^ { n } \right) ^ { 1 / n }$$ where $$a > 0$$ and $$n$$ is a positive integer then $$( f o f ) ( x )$$ is 

Let $$A = \{ 1,2,3 \}$$ . Which of the following functions on A is invertible?

If $$f ( x ) = \sin ^ { - 1 } ( \sin x ) + \cos ^ { - 1 } ( \sin x ) \text { and } \phi ( x ) = f ( f ( f ( x ) ) )$$ then $$\phi ^ { \prime } ( x )$$

$$f:R \rightarrow R$$ such that $$f(x)=\ell n(x+\sqrt {x^{2}+1})$$. Another function $$g(x)$$ is defined such that $$gof(x)=x\ \forall\ x \in\ R$$. Then $$g(2)$$ is -