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This problem, you're being asked to find the domain for the given function.
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Now, we have a couple of things going on here.
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First off, we're taking the square root in the expression.
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So we know that everything inside of our square root has to be greater than equal to zero.
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So we have to figure out when is 3 divided by 2x minus 18 going to be greater than are equal to 0.
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We have to figure out when it's positive.
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Well, the other issue that we have is we have a fraction.
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Remember, the denominator of our fraction cannot equal to zero.
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So we also have to figure out when is 2x minus 18 going to equal to zero? because we've got to make sure that it's not.
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So we'll solve the first part or the second part first because that'll be a little easier.
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So i'm going to add 18 to both sides.
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So 2x would equal to 18.
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And then we'll go ahead and divide both sides by 2.
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So we'll find that x is going to be equal to 9.
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So now we know that that would cause our denomity be 0, meaning that x cannot be equal to 9 in this case.
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So that's the first part that we have so far.
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So now we've got to go back and figure out when is this equation 3 divided by 2x minus 18, when is that going to be positive? because if it's positive, then it's going to be part of our domain...