Find the Domain

**james121515** · March 1st 2010, 01:35 PM

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

**Plato** · March 1st 2010, 01:55 PM

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 $f\text{ or }g$ .

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