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

$A$ function $f: R \rightarrow R$ satisfies the relation $f(x+y)=f(x) \cdot f(y), \forall x, y \in R$ and $f(x) \neq 0, \forall x \in R$. If $f$ is differentiable at $x=0$,$f^{\prime}(0)=4$,and $f(6)=3$,then $f^{\prime}(6)$ 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 $f(x_1) - f(x_2) = f\left( \frac{x_1 - x_2}{1 - x_1 x_2} \right)$ for $x_1, x_2 \in [-1, 1]$,then $f(x)$ is

Let $f: R \rightarrow R$ be defined by $f\left(\frac{x+y}{2}\right)=\frac{f(x)+f(y)}{2}$ for all $x$ and $y$. If $f^{\prime}(0)$ exists and equals $-1$ and $f(0)=1$, then $f(2)=$

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