Relations and F...

If $$f\left( 0 \right) = 0,f\left( 1 \right) =1 ,f\left( 2 \right) = 2$$ and $$f\left( x \right) = f\left( {x - 2} \right) + f\left( {x - 3} \right)$$ for $$x = 3,4,5.....$$ then $$f\left( 9 \right) = ?$$

If $$a\ne R$$ and the equation $$-3(x-[x])^2+2(x-[x])+a^2=0$$ ( where $$[x]$$ denotes the greatest integer $$\le x$$) has no integral solution, then all possible values of a lie in the interval : 

$${x\epsilon R:\frac{14x}{x+1}-\frac{9x-30}{x-4}<0}$$ is equal to 

$$f:\left( 0,\infty  \right) \rightarrow R$$ is continuous. If  $$F\left(x\right)$$ is a differentiable function such that $$F\left(x\right)= f\left(x\right), \forall x>0$$ and $$ f\left( { x }^{ 2 } \right) ={ x }^{ 2 }+{ x }^{ 3 }$$, then $$f\left(4\right)$$ equals 

If $$\left| { z }_{ 1 }-a \right| <a,\left| { z }_{ 2 }-a \right| <b,\left| { z }_{ 3 }-a \right| <c$$, $$(a,b,c\in R)$$ then $$\left| { z }_{ 1 }+{ z }_{ 2 }+{ z }_{ 3 } \right| $$ is

The domain of $$\dfrac { 10 ^ { x } + 10 ^ { - x } } { 10 ^ { x } - 10 ^ { - x } }$$ is

If $$R$$ is the relation from set $$A$$ to a set $$B$$ and $$S$$ is the relation from $$B$$ to a set $$C$$, then the relation $$SoR$$

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by :$$(x,y)\in\;R\; \rightarrow x$$ is relatively prime to y. Then, domain of R is

Let $$f(x)=$$max $$\{(1-x), (1+x), 2\}, \forall x\in R$$. Then?

If $$f ( x ) + 2 f ( 1 - x ) = x ^ { 2 } + 2 , \forall x \in R$$, then find $$f ( x )$$