If $f\left(x\right)=\frac{x^2-7x+10}{x^2+2x-8},$ for $x\in [-6,-3]$, then

If $f\left(x\right)=a{x}^2+bx+1,$ for $|x-1|\ge 3$

$=4x+5,$ for $-2<x<4$

is continuous everywhere then,

If $f\left(x\right)=\left\{\begin{array}{l}\frac{\left({16}^x-1\right)\left(9^x-1\right)}{\left({27}^x-1\right)\left({32}^x-1\right)}, \text{for} x\ne 0\\ k, \text{for} x=0\end{array}\right.$ is continuous at $x=0,$ then $k=$

If $f\left(x\right)=\left\{\begin{array}{l}\frac{{32}^x-8^x-4^x+1}{4^x-2^{x+1}+1}, \text{for} x\ne 0\\ k, \text{for} x=0\end{array}\right.$ is continuous at $x=0,$ then value of $k$ is

If $f\left(x\right)={\left(\frac{4+5x}{4-7x}\right)}^{\frac{4}{x}},$ for $x\ne 0$ and $f\left(0\right)=k,$ is continuous at $x=0,$ then $k$ is

If $f\left(x\right)=\left[x\right]$, (where $\left[.\right]$ represents greatest integer function) for $x\in \left(-1,2\right)$, then $f$ is discontinuous at

Discuss the continuity of the following function at the point(s) or on the interval indicated against them.

$f\left(x\right)=\frac{x^2-3x-10}{x-5}$, for $3\le x\le 6, x\ne 5$

$=10$, for $x=5$

$=\frac{x^2-3x-10}{x-5}$, for $6<x\le 9$.

Discuss the continuity of the following function at the point(s) or on the interval indicated against them.

$f\left(x\right)=2x^2-2x+5$, for $0\le x\le 2$

$=\frac{1-3x-x^2}{1-x}$, for $2<x<4$

$=\frac{x^2-25}{x-5}$, for $4\le x\le 7$ and $x\ne 5$

$=7$, for $x=5$.