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Question 783960: m^2+2m-24/m^2-3m
I have to find the domain for the problem write it in set notation and determine if it has an excluded value and explain why or why not.
I can factor the top portion to (m+6)(m-4) but i don't know what to do with the bottom. and i honestly don't know what domain, set notation and excluded value mean. i haven't had a math class in years and feel overwhelmed just looking at this problem. any help will be much appreciated.
Thank you
Faith Rayborn
faithdrayborn1@hotmail.com
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The domain of a function is the set of real numbers for which the function is defined. For polynomial functions, that is always the entire set of real numbers. For rational functions, such as your example, it is the set of real numbers with any values that would cause the denominator polynomial to equal zero excluded. For functions including radicals with an even index (square root, 4th root, 6th root, and so on), the domain is restricted to those values that make the radicand non-negative (that is to say, greater than or equal to zero).
The procedure for a radical function such as your example is to take the denominator expression, set it equal to zero, then solve for all real roots. Then the domain is the set of all real numbers except for those real zeros you found for the denominator.
Specifically, in this case:
\ =\ \frac{m^2\ +\ 2m\ -\ 24}{m^2\ -\ 3m})
So set the denominator equal to zero:
And solve:
\ =\ 0)
Hence  and  are excluded.
\ =\ \left\{m\ \in\ \mathbb{R}\ |\ m\ \not =\ 0\ \large{ & }\LARGE\ m\ \not =\ 3\right\})
Read: "The domain of f is the set of all numbers  contained in the real numbers such that is not equal to zero and is not equal to 3."
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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