The range of the real valued function $f(x)=\left(\frac{x^2+2 x-15}{2 x^2+13 x+15}\right)$ is

$f: R \rightarrow R$ is defined by $f(x+y)=f(x)+12 y, \forall x, y \in R$. If $f(1)=6$, then $\sum_{r=1}^n f(r)=$

The domain of the real valued function $f(x)=\sqrt{2+x}+\sqrt{3-x}$ is

Let $f(x)=3+2 x$ and $g_n(x)=(f \circ f \circ f o \ldots$ in times $)(x)$, $\forall n \in N$ if all the lines $y=g_n(x)$ pass through a fixed point $(\alpha, \beta)$, then $\alpha+\beta=$