If $3 f(x) - f\left(\frac{1}{x}\right) = 8 \log_2 x^3$ for $x > 0$,then $f(2), f(4), f(8)$ are in

Let $a, b, c \in \mathbb{R}$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f(x + y) = f(x) + f(y) + xy, \forall x, y \in \mathbb{R}$,then $\sum_{n=1}^{10} f(n)$ is equal to:

Let $R$ be the set of all real numbers. The number of continuous functions $f: R \rightarrow R$ such that for all real $x$,$f(x) + f(2x) = 0$ is

If $f(1)=0$ and $f(n+1)-f(n)=5n$ for all $n \in N$, then $f(n)=$

Let $f(x + y) = f(x) + f(y)$ for all $x, y \in R.$ Then:

Let $f: N \rightarrow N$ be a function such that $f(m+n)=f(m)+f(n)$ for every $m, n \in N$. If $f(6)=18$ then $f(2) \cdot f(3)$ is equal to :