If $f(x) = x - \frac{1}{x}$,$x \neq 0$,then $3f(x) =$

Let $f : R - \{0, 1\} \rightarrow R$ be a function such that $f(x) + f\left(\frac{1}{1-x}\right) = 1 + x$. Then $f(2)$ is equal to:

Let $f$ and $g$ be functions satisfying $f(x+y)=f(x)f(y)$,$f(1)=7$ and $g(x+y)=g(xy)$,$g(1)=1$ for all $x, y \in \mathbb{N}$. If $\sum_{x=1}^{n} \left(\frac{f(x)}{g(x)}\right) = 19607$,then $n$ is equal to:

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

Find $\sum_{t=1}^{39} f(t)$ if $f: R \rightarrow R$ is defined as $f(x+y)=f(x)+f(y)$ for all $x, y \in R$ and $f(1)=7$.

Let $f(x)$ be a differentiable function which satisfies the equation $f(xy) = f(x) + f(y)$ for all $x > 0, y > 0$. Then $f'(x)$ is equal to: