Question

Would someone please help me see how to work out the problem f/g, when f(x) = square root of 3-x, and g(x) = square root of x^2-1 please? and I need to figure out the domain. Thank you

Answer 1

\(\frac{f(x)}{g(x)}=\frac{\sqrt{3-x}}{\sqrt{x^2-1}}\).
Domain:
\(\left\{\begin{matrix}
3-x\geqslant0\\
x^2-1>0
\end{matrix}\right.\), \(\left\{\begin{matrix}
x\leqslant3\\
x\in(-\infty,-1)\bigcup(1,+\infty)
\end{matrix}\right.\) \(\Rightarrow x\in(-\infty,-1)\bigcup(1,3]\)