SOLUTION: find the domain of f(x)= (log(x-1))/ (sqrt(6-3x))
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Question 627000: find the domain of f(x)= (log(x-1))/ (sqrt(6-3x))
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \frac{\log(x\,-\,1)}{\sqrt{6\,-\,3x}})
The domain is the set of allowable inputs. First, the logarithm function is defined for strictly positive arguments. Hence, )
is restricted by 
which is to say 
Further, the square root function is defined for non-negative arguments, so considering only the square root function, is restricted by 
. However, since the square root function is in the denominator of the rational function, the value zero for the square root function must also be excluded from the domain. Hence we must only include 
, which is to say 
.
Putting the two restrictive statements together we get:
\ =\ \left\{x\ \in\ \mathbb{R}\ |\ 1\ <\ x\ <\ 2\right\})
John
My calculator said it, I believe it, that settles it
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