SOLUTION: Whats the domain of f(x)= {{{ sqrt( (x+2)/(x^2-8x+15) ) }}}

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Question 760469: Whats the domain of f(x)= +sqrt%28+%28x%2B2%29%2F%28x%5E2-8x%2B15%29+%29+
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Finding and checking around critical points would be the best way. The function is f%28x%29=sqrt%28%28x%2B2%29%2F%28%28x-3%29%28x-5%29%29%29. Critical points are x element of {-2, 3, 5}. x is allowed to be -2, but is NOT allowed to be 3 or 5. For the rest of finding the domain, check the intervals which the critical points create.

The intervals to check are these:
(-infin, -2]
[-2, 3)
(3, 5)
(5, infin)
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If a value in the interval makes the function true, the the interval is part of the domain; if not true, then it is excluded from the domain.