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Thread: Help with a problem about finding the domain of a function?

  1. #1
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    Help with a problem about finding the domain of a function?

    Hello everyone. We're supposed to find the domain of this function (attached picture) and when I searched the net the answer said it's x=-1. When I tried solving it, I came up with x≤1 and x≥-1... Can someone please guide me? Thank you very much!
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  2. #2
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    Re: Help with a problem about finding the domain of a function?

    This is exactly the kind of problem that will cause problems for people who are used to applying formulas without thinking about the problem and whether the formula is appropriate. Assuming that we are dealing with real numbers, the domain of the square root function is $\displaystyle x\ge 0$. Here, we have $\displaystyle \sqrt{-|x+1|}$ so we need $\displaystyle -|x+ 1|\ge 0$. That is the same as $\displaystyle |x+ 1|\le 0$. Absolute value is never negative but is 0. We cannot have $\displaystyle |x+ 1|< 0$ but we can have $\displaystyle |x+ 1|= 0$. That happens if and only if x= -1.
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