find the domain and range

Mathematics
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f(x)= negative square root of x+3

Jul 22nd, 2015

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Find the domain and Range f (x)=square root x-3 divided by 6-3x ... will always be negative (because x>=3 this means 6-3x<-3) except when x=3 

Squares need to be >=0. Thus
x-3>=0
Implies x must be >=3
We cannot divide by zero, thus 6-3x cannot =0.
Find where that is the case. 6=3x ->x=2

So we have x cannot be 2 and must be >=3.
We thus have the following domain in interval notation: [3,infinity).
Since the numerator will always be positive or =0, we need only look at the denominator and see that this will always be negative (because x>=3 this means 6-3x<-3) except when x=3 (which gives y=0).
We thus have the follow range in interval notation: (-infinity,0]

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 22nd, 2015

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