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

$A$ function $f: R \rightarrow R$ satisfies $f\left(\frac{x+y}{3}\right) = \frac{f(x)+f(y)+f(0)}{3}$ for all $x, y \in R$. If the function $f$ is differentiable at $x=0$, then $f$ is:

If $g:[-2, 2] \to R$ where $g(x) = x^3 + \tan x + \left[ \frac{x^2 + 1}{P} \right]$ is an odd function,then the value of the parameter $P$ is:

Let $f$ be a function satisfying $f(xy) = \frac{f(x)}{y}$ for all positive real numbers $x$ and $y.$ If $f(30) = 20,$ then the value of $f(40)$ is-

If $f(x - y) + f(x + y) = 2f(x)f(y)$ for all $x, y \in R$, then $f(x)$ is .....

Let $f$ be a function defined on the set of all positive integers such that $f(xy) = f(x) + f(y)$ for all positive integers $x, y$. If $f(12) = 24$ and $f(8) = 15$,then the value of $f(48)$ is: