Answer
a.$\displaystyle \quad q(x)=\frac{x-1}{\sqrt{10-x}}$
b.$\quad [0,10)$
c.$\quad 0$
Work Step by Step
$a.$
$q=\displaystyle \frac{f}{g}$ is the function specified by $q(x)=\displaystyle \frac{f(x)}{g(x)}$
$q(x)=\displaystyle \frac{x-1}{\sqrt{10-x}}$
$b.$
See Note on Domains p.70-71
Domain of $f/g$:
All real numbers $x$ simultaneously in the domains of $f$ and $g$ such that $g(x)\neq 0$
Given the domains of $v$ and $g$,
the domain of $q$ is the set
$[0,10]$ for which $\sqrt{10-x}\neq 0$,
$[0,10]$ for which $x\neq 10$,
That is, $0 \leq x <10$,
or written in interval form; $[0,10)$
$\mathrm{c}.$
$q(1) =\displaystyle \frac{1-1}{\sqrt{10-1}}=\frac{0}{3}=0$
