Answer:
x≠5
or
[tex]\:\left(-\infty \:,\:5\right)\cup \left(5,\:\infty \:\right)[/tex]
Step-by-step explanation:
Both the answers above are correct, but the second is written in interval notation; there are also other ways to represent this same domain. The domain of a function are the possible x-values.
To find the domain, you must first find the new function. We are looking for [tex]\frac{f}{g} (x)[/tex]. This means you need to divide f(x)'s rule by g(x)'s rule. This equals [tex]\frac{f}{g}(x)=\frac{x^{2} -25}{x-5}[/tex]. To find the domain, remember that functions are undefined when the denominator is 0. So, x cannot equal 5 because this would make the denominator 0.
