What is the result of this inequality among these three options?

I

itsrayex

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I have solved this inequality correctly I think. I am inclined to say the result is A but option C also makes me think. I know (-1,1) is not included in the domain but according to the little "scheme" I drew, the function is positive in that interval and therefore I would consider it as part of the result. If this is not the case, then I assume that for inequalities the solution ALWAYS has to be according to the domain, regardless of what the scheme says. Is that the case?

(I am not that good at math and I am just trying to pass a test and I don't have a lot of time, this is why I approach math exercises in such a mechanical way, with a learnt method, rather than reasoning. Knowing the reasoning behind the steps would help me remember the steps for sure tho)

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itsrayex said:
I have solved this inequality correctly I think. I am inclined to say the result is A but option C also makes me think. I know (-1,1) is not included in the domain but according to the little "scheme" I drew, the function is positive in that interval and therefore I would consider it as part of the result. If this is not the case, then I assume that for inequalities the solution ALWAYS has to be according to the domain, regardless of what the scheme says. Is that the case?

(I am not that good at math and I am just trying to pass a test and I don't have a lot of time, this is why I approach math exercises in such a mechanical way, with a learnt method, rather than reasoning. Knowing the reasoning behind the steps would help me remember the steps for sure tho)

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Can you explain why you aren't sure which of (a) and (c) is correct? And why you think each of them could be?

I would draw a similar diagram (though I mark the sign of each factor in each interval, rather than just graphing where it is positive).

To answer your specific question about (-1,1), a function can't be positive when it is not defined, so I would label that interval as "u" (undefined) rather than "+".

Then, I would add to the diagram labels indicating the points at which the function is equal to zero, or is undefined; and then for each of the four labeled intervals, and each of the three labeled points, decide whether it belongs in the solution set.

Understanding actually saves time. Tell me what you now think the solution is.
 
Nice little problem.
What's that under the square root sign ?
x^t-1 perhaps?
 
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