Posted by MUFFY on Monday, September 21, 2009 at 8:41pm.
Determine the domain of the following function: f(x)=sqrt x7/x^25x6
I think the domain is
[7,all real numbers)
Can you please tell me if this is correct?

PRECALC  MathMate, Monday, September 21, 2009 at 11:49pm
You have to be more generous with your parentheses. As is the function does not seem to be properly defined.
It could be
f(x) = sqrt( (x7)/(x²5x6) )
or
g(x) = sqrt(x7) / (x²5x6) )
I assume it is f(x). If it is g(x), you can proceed along the same lines, and post your results for confirmation.
f(x) can be rewritten as:
f(x) = sqrt( (x7)/((x2)(x3)) )
which tells us that
1. at x<7, the numerator becomes negative.
2. The denominator is a parabola which has zeroes at x=2 and x=3.
3. The denominator is negative between x=2 and x=3. It is positive elsewhere.
From 1 and 3, we conclude that the fraction inside the square radical is
1. negative when x<2,
2. positive when 2<x<3
3. negative when 3<x<7
4. positive when x>7
Also, there are two vertical asymptotes at x=2 and x=3 which should be removed from the domain of f(x).
Therefore the domain of f(x) is:
(2,3)∪(7,∞) 
PRECALC  MUFFY NEEDS MORE HELP, Tuesday, September 22, 2009 at 5:32pm
Actually, there are no parenthesis. The problem is how I wrote it but
sqrt x7 is over x^2 5x  6
I factored it to (x6) (x+1) 
PRECALC  MathMate, Tuesday, September 22, 2009 at 5:40pm
" Actually, there are no parenthesis. The problem is how I wrote it but
sqrt x7 is over x^2 5x  6 "
You have to be more generous with parentheses. Whenever a fraction is transcribed to a single line, you will need to insert parentheses around the numerator AND the denominator to avoid ambiguity.
From what you described, you would write the expression as
sqrt(x7)/(x^2 5x  6)
otherwise it can be (unlikely) interpreted as
sqrt(x) 7/x² 5x 6
which is not a normal function.
Back to the function:
f(x) = sqrt(x7)/(x^2 5x  6)
=sqrt(x7)/((x2)(x3))
you have already correctly identified the donmain [7,∞).
The only other considerations required would be to exclude the two singular points (x=2 and x=3) from the domain.
Post your results for checking if you wish. 
PRECALC  MUFFY NEEDS MORE HELP, Tuesday, September 22, 2009 at 11:44pm
Thanks I didn't realize how to type it when one is over the other. I will keep it in mind.