$f: R \rightarrow R$ 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 $f$ be a function such that $f(x) + 3f\left(\frac{24}{x}\right) = 4x$,where $x \neq 0$. Then $f(3) + f(8)$ is equal to:

If $f$ is a function satisfying $f(x+y)=f(x) f(y)$ for all $x, y \in N$ such that $f(1)=3$ and $\sum\limits_{x = 1}^n {f(x) = 120}$,find the value of $n$.

$A$ real-valued function $f(x)$ satisfies the functional equation $f(x - y) = f(x)f(y) - f(a - x)f(a + y)$,where $a$ is a given constant and $f(0) = 1$. Then $f(2a - x)$ 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) = $

If $f(x) = \frac{x}{x - 1} = \frac{1}{y}$,then $f(y) = $