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Question 653884: Find the domain, in interval notation, for the following function:
f(x)=(x^2-4x-21)/sqrt(2x-5)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You have two things to consider with the given function. Anytime you
have a function that has a denominator, you must not allow the
denominator to equal zero. Hence, any value that would make the
denominator zero would have to be excluded from the domain. Also, you
have a radical. Anytime you have a radical with an even index (square
root, 4th root, 6th root, etc.) and you have a function that is mapped
to the real numbers, then you must ensure that the radicand (the part
under the radical) is non-negative.
So in your case, to keep the radicand from being less than zero, you would solve
But since this radical is in the denominator, it can't be zero either,
so your domain is the interval described by the solution set of:
Just as an Oh, By The Way, if this function were mapped to the complex
numbers then the only value exluded from the domain would be zero
John
My calculator said it, I believe it, that settles it
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