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:

If $f(x) + 2f(1/x) = 3x$ for $x \neq 0$ and $S = \{x \in R : f(x) = f(-x)\}$,then $S$:

If $(f(x))^2 = f(x^2) + f(1)$ holds good,then find $f(x)$.

Let $f: R \rightarrow R$ be a function which satisfies $f(x+y)=f(x)+f(y)$ for all $x, y \in R$. If $f(1)=2$ and $g(n)=\sum_{k=1}^{n-1} f(k)$ for $n \in N$,then the value of $n$ for which $g(n)=20$ is:

If $f(x)$ is a function satisfying the condition $f(x) = \frac{1}{3}\left[ f(x + 6) + \frac{6}{f(x + 7)} \right]$ and $f(x) \geq 0$ for all $x \in R$. If $\lim_{x \to \infty} f(x) = \sqrt{m}$,then the value of $m$ is:

If $f(x)$ is a polynomial function satisfying $f(x) \cdot f(\frac{1}{x}) = f(x) + f(\frac{1}{x})$ and $f(4) = 65$,then the value of $f(6)$ is: