How do you find the domain of $g (x) = \frac{x}{x^{2} - 5 x}$ $g(x)= x/(x^2-5x)$ ?

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Answer 1 · 2017-10-25T16:03:27

$x in RR, x != 0,5$

The domain is the range of $x$ values a function can take.

The numerator of $g(x)$ is simply $x$ so it doesn't really matter what it is.

The denominator is more complex because we know that we can never divide by $0$ .

If the denominator is $0$ , then

$x^2 - 5x = 0$

$x(x-5) = 0$

so

$x = 0, 5$

In which case the domain is $x in RR, x != 0, 5$

How do you find the domain of g(x)= x/(x^2-5x)g(x)=xx2−5xg(x)= x/(x^2-5x)?