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Question 652251: Find the domain of the function g(x)=x+7/x^2-36
Any help would be appreciated!
Thank you.
Rae Henson
Answer by Shana-D77(132)   (Show Source):
You can put this solution on YOUR website! "Finding the domain" is a fancy pants way of saying "find where the denuminator is not zero"
(x + 7)/(x^2 - 36) factors to:
(x + 7)/(x - 6)(x + 6)
If x = 6, the denominator would equal zero (6 - 6)(6 + 6) = (0)(12) = 0. So, 6 is excluded. Same for -6.
Domain is "all Real numbers except 6 and -6"
Now, if one of those ( ) in the denominator cancelled with the (x + 7) in the numerator, we could cancel that parenthesis and have only one exception to the domain. Example: (x + 6)/(x + 6)(x - 6). The (x + 6)s cancel so that the domain would be "all Reals except 6 (only)."
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