Functions Test ...

State which of the following defines a mapping from A to B, if $$A={a,b,c,}$$ and $$B={x,y,z}.$$

If  $$f ( x ) = \sqrt { x ^ { 2 } + 1 } , g ( x ) = \dfrac { x + 1 } { x ^ { 2 } + 1 }$$  and  $$h ( x ) = 2 x - 3 ,$$  then  $$f ^ { \prime } \left( h ^ { \prime } \left( g ^ { \prime } ( x ) \right) =\right.$$

$${ f }:{ R }\rightarrow { R }$$  where  $$f ( x ) = \dfrac { x ^ { 2 } + a x + 1 } { x ^ { 2 } + x + 1 }.$$  Complete set of values of  $$'a'$$  such that  $$f ( x )$$  is onto to is :

The domain of $$f(x) = \sin^{-1} log_2 (x^2/2)$$ is

The number of integral values of  $$x$$  in the domain of function  $$f$$  defined as  $$f(x)=\sqrt { \ln { | } \ln { | } x|| } +\sqrt { 7|x|-|x|^{ { 2 } }-10 } $$  is :

The domain and the range of $$f(x) = \cos^{-1} \sqrt {\log_{[x]} \left (\dfrac {|x|}{x}\right )}$$, where $$[\cdot ]$$ denotes the greatest integer function, are respectively.

Choose correct answer (s) from given choice
If f(x) = x + 4, g (x) = 5x and h(x) = 12/x. Find the value of $${ f }^{ -1 }(g(h(6)))$$ 

If f(x)=x+tanx and g(x) is inverse of f(x) then g'(x) is equal to 

The domain of $$f(x)=\sqrt { -x^2 }$$ is 

For the function $$F(x)=\sqrt { { 4-x }^{ 2 } } +\sqrt { { x }^{ 2 }-1 } $$