$f: R \rightarrow R$ is defined by $f(x+y)=f(x)+12y, \forall x, y \in R$. If $f(1)=6$,then $\sum_{r=1}^n f(r)=$

Let $f : R \rightarrow R$ be a continuous function such that $f(3x) - f(x) = x$. If $f(8) = 7$,then $f(14)$ is equal to.

If $f : R \to R$ is such that $f(x + y) = f(x) + f(y)$ for all $x, y \in R$,$f(1) = 7$ and $\sum_{r=1}^{n} f(r) = 14112$,then $n$ is equal to:

If $f : \mathbb{Z} \rightarrow \mathbb{Z}$ is defined by $f(x) = x^{9} - 11 x^{8} - 2 x^{7} + 22 x^{6} + x^{4} - 12 x^{3} + 11 x^{2} + x - 3, \forall x \in \mathbb{Z}$,then $f(11) = $

Let $f: N \rightarrow R$ be such that $f(1)=1$ and $f(1)+2 f(2)+3 f(3)+\ldots+n f(n)=n(n+1) f(n)$ for all $n \in N, n \geq 2,$ where $N$ is the set of natural numbers and $R$ is the set of real numbers. Then,the value of $f(500)$ is

If $f(f(0)) = 0$,where $f(x) = x^2 + ax + b$ and $b \neq 0$,then $a + b =$