If $f: R-\{0\} \rightarrow R$ is defined by $3 f(x)+4 f\left(\frac{1}{x}\right)=\frac{2-x}{x}$, then find the value of $f(3)$.

The function $f(x) = x - [x]$,where $[x]$ denotes the greatest integer function,is:

Let $f: R \rightarrow R$ be a function defined by $f(x) = \frac{2x+1}{3}$. If $\alpha$ is an element in the domain of $f$ whose image is $\frac{1}{\alpha}$,then the sum of all possible values of such $\alpha$ is

If $f(x)$ satisfies $f(7 - x) = f(7 + x)$ for all $x \in R$ such that $f(x)$ has exactly $5$ real roots which are all distinct,and the sum of the real roots is $S$,then $S/7$ is equal to:

The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find $t(28)$.

If $f(x)$ is a polynomial function satisfying $f(x) \cdot f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$ and $f(4)=257$,then $f(3)=$