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

1 Answer
May 24, 2017

Answer:

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

Explanation:

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#