If $\phi (x) = a^x$,then $\{ \phi (p) \} ^3$ is equal to

If $f(x_1) - f(x_2) = f\left( \frac{x_1 - x_2}{1 - x_1 x_2} \right)$ for $x_1, x_2 \in [-1, 1]$,then $f(x)$ is

Let $f: \mathbb{R} - \{0\} \rightarrow (-\infty, 1)$ be a function satisfying $f(x)f(\frac{1}{x}) = f(x) + f(\frac{1}{x})$. If $f(x)$ is a polynomial of degree $2$ and $f(K) = -2K$,then the sum of squares of all possible values of $K$ is:

Let $f: N \times N \rightarrow N$ be a function such that $f(1,1)=2$,$f(m+1, n)=f(m, n)+2(m+n)$,and $f(m, n+1)=f(m, n)+2(m+n-1)$ for all $m, n \in N$. Find the value of $f(2,2)$.

Suppose $f : R \rightarrow (0, \infty)$ be a differentiable function such that $5f(x + y) = f(x) \cdot f(y), \forall x, y \in R$. If $f(3) = 320$,then $\sum_{n=0}^5 f(n)$ is equal to:

If $f(x)$ is a differentiable function such that $f(xy) = f(x) + f(y)$ for all $x, y > 0$,then $f(e) + f(1/e) = ?$