How do you find the domain of $f(x)=sqrt((x^2) -9x)$ ?

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Answer 1 · 2017-05-24T18:51:27

Domain of $x$ is $(-oo, 0]$ and $[9, oo)$

Well we know that for $f(x)inRR^n$ :
$x^2-9x>=0$

Since that's the only inequality, solving for that will give the domain.
$x^2>=9x$
$x>=9$

And when $x>0$ , $x^2-9x>=0$ will always hold true, so:
$x<=0$

graph{sqrt(x^2-9x) [-28.42, 36.53, -1.3, 31.18]}

So, in interval notation, the domain of $x$ is:

$(-oo, 0]$ and $[9, oo)$
And $f(x)>=0$

How do you find the domain of f(x)=sqrt((x^2) -9x) f(x)=sqrt((x^2) -9x) ?