Define a function $f(x) = \frac{16x^2 - 96x + 153}{x - 3}$ for all real $x \neq 3$. The least positive value of $f(x)$ is

Let $R-(\alpha, \beta)$ be the range of $f(x) = \frac{x+3}{(x-1)(x+2)}$. Then,the sum of the intercepts of the line $\alpha x + \beta y + 1 = 0$ on the coordinate axes is:

For $x \in \mathbb{R}$,if $f(x) = \sqrt{\log_{10}\left(\frac{3-x}{x}\right)}$,then the domain of $f$ is

The range of $f(x) = \cos[x]$ for $-\frac{\pi}{4} < x < \frac{\pi}{4}$ (where $[.]$ represents the greatest integer function less than or equal to $x$) is

If $x$ is real,then the range of $\frac{x^2+2x+1}{x^2+2x+7}$ is

If the real valued function $f(x)=\sin ^{-1}(x^2-1)-3 \log _3(3^x-2)$ is not defined for all $x \in(-\infty, a] \cup(b, \infty)$, then $3^a+b^2=$