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

Let $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$. Suppose that $f(3)=3$ and $f^{\prime}(0)=11$,then $f^{\prime}(3)$ is given by

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) = $

The function $f$ satisfies the functional equation $3f(x) + 2f\left( \frac{x + 59}{x - 1} \right) = 10x + 30$ for all real $x \neq 1$. The value of $f(7)$ is

Given the function $f(x) = \frac{a^x + a^{-x}}{2}, (a > 2)$,then $f(x + y) + f(x - y)$ is equal to

If $f(x + y) = f(x)f(y)$ and $\sum_{x=1}^{\infty} f(x) = 2$,where $x, y \in N$ and $N$ is the set of all natural numbers,then the value of $\frac{f(4)}{f(2)}$ is