Relations and F...

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

$$f : R \rightarrow R$$  defined by  $$f ( x ) = \dfrac { x } { x ^ { 2 } + 1 } , \forall x \in R$$  is

If f (x) = cosx and g (x) = x$$^2$$ then (gof) (x) is ....

Suppose that $$g(x)=1+\sqrt { x } and\quad f(g(x))=3+2\sqrt { x } +x\quad then\quad f(x)\quad is$$

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

If the operation * is defined as $$\left( a\times b \right) ={ a }^{ 2 }+{ b }^{ 2 }$$ then $$\left( 3\times 4 \right) =5$$ is

Consider the binary operation $$*$$ on $$Q$$ defined by $$x*y=1+12x+xy,x,y\rightarrow Q$$ then $$2*3$$ equals

Let A=(5,6); how many binary operations can be defined on this set?

If =$$f=\left\{ (-2,4),(0,6),(2,8) \right\} $$ and 
$$g=\left\{ (-2,-1),(0,3),(2,5) \right\} $$, then 
$$\left( \frac { 2f }{ 3g } +\frac { 3g }{ 2f }  \right) (0)=\quad $$

Number of solution of the equation  $$f ( x ) = g ( x )$$  are same as number of point of intersection of the curves $$y = f ( x )$$  and  $$y = g ( x )$$  hence answer the following question.
Number of the solution of the equation  $$x ^ { 2 } = | x - 2 | + | x + 2 | - 1$$  is