Functions Test ...

Consider the function $$f\left( x \right) ={ e }^{ x }$$ and $$g\left( x \right)=\sin ^{ -1 }{ x } $$, then which of the following is/are necessarily true.

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

Domain of function $$y=\sqrt{\log_{0.6}\left(\dfrac{x-1}{x+5}\right)}\cdot\dfrac{1}{(x^2-49)}$$ is?

Let N be the set of natural numbers and two functions f and g be defined as
and g(n)=$$n-{ \left( -1 \right)  }^{ n }$$ then fog 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

$$f (x) = x^4 - 10x^3 + 35x^2 - 50x + c$$ is a constant. the number of real roots of . f (x) = 0 and 
f'' (x) = 0 are respectively 

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

Let f(x+y)=f f(x) f(y) and  f(x) =1+x g(x) G(x), where $$\underset { x\rightarrow 0 }{ lim } g\left( x \right) =a and \underset { x\rightarrow 0 }{ lim } G\left( x \right) =b,$$ then f' (x) is equal to

$$f:N\rightarrow N\quad where\quad f\left( x \right) =x-{ (-1) }^{ x }$$, then 'f' is

Let (X) be a function satisfying f' (X) = f (X) with f (0) = 1 and g (X) be a function that satisfies f (X) + g (x) = $${ x }^{ 2 },$$ Then the value of the integral $$\int _{ 0 }^{ 1 }{ f } (x)\quad g\quad (x)\quad dx,\quad is$$