Relations and F...

$$f(x)=(x-1)(x-2)(x-3)(x-4)$$. Then out of three roots of $$f'(x)=0$$

If f (x+y).f(y) for all x,y, where f'(0)=3 and f(4)=2 then f'(4) is equal to

If  $$f \left( \dfrac { x + y } { 2 } \right) = \dfrac { f ( x ) + f ( y ) } { 2 }$$  for all  $$x , y \in R$$  and  $$f ^ { \prime } ( o ) = - 1 , f ( o ) = 1$$  then  $$f(2)=$$

If $$z$$, satisfies the condition that $$\dfrac { w-\overline{w}z }{ 1-z }$$ is purely real, then the set of values of $$z$$ is

Let $$R$$ be a relation on $$N$$ defined by $$x+2y=8$$. The domain of $$R$$ is

The value of $$f(1)$$ is

Let $$A\equiv \left\{1,2,3,4\right\},\ B\equiv \left\{a,b,c\right\}$$, then number of function from $$A\rightarrow B$$, which are not onto is

If domain of $$y = f\left( x \right)$$ is $$ \left[ { - 3,\,\,2} \right]$$ then domain of $$y = f\left( {\left| {\left[ x \right]} \right|} \right)$$ is

If $$x \epsilon$$ { $$1, 2, 3, ......,9$$} and $$f_n(x)=xxx.....x (n $$digit) then $$f_n ^2(3) + f_n(2)$$ is equal to 

Let  $$R = \{ ( 3,3 ) , ( 6,6 ) , ( 9,9 ) , ( 6,12 ) , ( 3,9 ) , ( 3,12 ) , ( 3,6 ) \}$$  be a relation on the set  $$A=\{ 3,6,9,12\} .$$  Then the relation  $$R ^ { - 1 }$$  is