Question

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of (StartFraction f Over g EndFraction) (x)?

Answer 1

x≠5

or

`\:\left(-\infty \:,\:5\right)\cup \left(5,\:\infty \:\right)`

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
`(f)/(g) (x)`. This means you need to divide f(x)'s rule by g(x)'s rule. This equals
`(f)/(g)(x)=(x^(2) -25)/(x-5)`. 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.