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Math Help - Domain and Range question

  1. #1
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    Domain and Range question

    Hi,

    New to this site and hoped to get some advice with a question from first year Uni.

    Find the domain and range of:

    y  \f=\sin \left( \frac1{x+1} \right) + \exp \left( \frac1{x+1} \right)

    And explain if it has an inverse or not.

    We've done a over view of domains and ranges but I can't see any example quite like this in any of our notes or text books.

    I think the Domain is all Real numbers except x= -1 as function would not be well defined. The range, well, sine function will be [-1,1] and not sure of the exponential and when they are combined what happends. I've graphed this on Maple and don't know how to interpret the function.

    Any pointers and advice would be greatly appreciated.

    Thanks,

    Felix
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Domain and Range question

    You know that the domain of \sin(x) is \mathbb{R}, but now you have \sin\left(\frac{1}{x+1}\right) therefore you have to exclude the values wherefore the denominator becomes equal to 0 (same for the exp(...)).
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  3. #3
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    Re: Domain and Range question

    The only number that makes the denominators 0 is x = -1 as I mentioned. Is this not correct?
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  4. #4
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    Re: Domain and Range question

    i think the domain is R-{-1}
    and the range is R-[-1 ,-infinity)
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  5. #5
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    Quote Originally Posted by FelixHelix View Post
    Hi,

    New to this site and hoped to get some advice with a question from first year Uni.

    Find the domain and range of:

    y  \f=\sin \left( \frac1{x+1} \right) + \exp \left( \frac1{x+1} \right)

    And explain if it has an inverse or not.

    We've done a over view of domains and ranges but I can't see any example quite like this in any of our notes or text books.

    I think the Domain is all Real numbers except x= -1 as function would not be well defined. The range, well, sine function will be [-1,1] and not sure of the exponential and when they are combined what happends. I've graphed this on Maple and don't know how to interpret the function.

    Any pointers and advice would be greatly appreciated.

    Thanks,

    Felix
    Your domain is correct. To get the range, I suggest you first attempt to sketch each function seperately (the sine and the exp) and then add the graphs together using addition of ordinates ....

    Quote Originally Posted by prime View Post
    i think the domain is R-{-1}
    and the range is R-[-1 ,-infinity)
    Your range is wrong.
    Last edited by mr fantastic; October 16th 2011 at 12:25 PM. Reason: Merged posts.
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  6. #6
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    Re: Domain and Range question

    Also sketch the graph of 1/(x+1).

    The sine & exponential functions are used with very "large" negative as well as positive numbers.
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