1. ## Find the Domain

If $f(x)=\sqrt{x+4}$ and $g(x)=\sqrt{x-1}$, find the domain of $\,\frac{f}{g}$
$\left(\frac{f}{g}\right)(x)=\frac{\sqrt{x+4}}{\sqr t{x-1}}=\sqrt{\frac{x+4}{x-1}}$

So a radical is only when the value of the expression is greater than $0$, I would have thought that to find the domain, all I need to do is solve this rational inequality $\frac{x+4}{x-1}\geq 0$, whose solution is $(-\infty, -4]\cup (1, \infty)$, but, my solution manual says that the domain is actually $(1, \infty)$. Why is this so?

Thanks ,

James

2. Originally Posted by james121515
If $f(x)=\sqrt{x+4}$ and $g(x)=\sqrt{x-1}$, find the domain of $\,\frac{f}{g}$
$\left(\frac{f}{g}\right)(x)=\frac{\sqrt{x+4}}{\sqr t{x-1}}=\sqrt{\frac{x+4}{x-1}}$

my solution manual says that the domain is actually $(1, \infty)$. Why is this so?
The manual is correct.
$(-\infty,-4)$ is not a subset of the domain of either $f\text{ or }g$.