SOLUTION: please help im studying for my test and I cant do this problem I need to find the domain: f(x)={{{sqrt(2x+12)/(x^2-9x+14)}}}

Question 348860: please help im studying for my test and I cant do this problem I need to find the domain: f(x)=
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the domain: f(x)= sqrt(2x+12)/(x^2-9x+14)
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Two things to consides:
1st: 2x+12 must not be negative
2x+12 >= 0
x >= -6
---------------------
2nd: x^2 - 9x + 14 must not be zero
Solve x^2-9x+14 = 0
(x-7)(x-2) = 0
x cannot be 2 and cannot be 7
------
Domain: All Real Numbers >=-6 excluding
x = 2 and x = 7.
========================================
Domain: [-6,2)U(2,7)U(7,+oo)]
========================================
Cheers,
Stan H.
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