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Math Help - [SOLVED] Find the domain and range

  1. #1
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    [SOLVED] Find the domain and range

    What is the domain and range of this function?
    ln(e^(2x-1))

    i dont know if my answer is right but i got x is not 1/2
    and y = real numbers??


    does this graph look like a normal log one?

    i plug in numbers and i keep getting a diagonal line?
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  2. #2
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    Quote Originally Posted by NeedHelp18 View Post
    What is the domain and range of this function?
    ln(e^(2x-1))

    i dont know if my answer is right but i got x is not 1/2
    and y = real numbers??
    When x=\frac12, you have \ln\left(e^{2x-1}\right)=\ln e^0=\ln1=0\text. Why are you excluding that from the domain?

    does this graph look like a normal log one?

    i plug in numbers and i keep getting a diagonal line?
    What is \ln e^n? Or in general, \log_aa^n? Hint: the natural logarithm and the natural exponential function are inverses of each other.
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    i am lost now

    so what would be the domain?

    all real numbers?

    and is my range correct?
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    Quote Originally Posted by NeedHelp18 View Post
    i am lost now

    so what would be the domain?

    all real numbers?
    Yes. e^x is defined for all real x, its range is (0,\infty), and \ln x is defined for those values.

    and is my range correct?
    Yes. The range of e^x covers the entire domain of the natural logarithmic function and the range of the natural logarithmic function is (-\infty,\infty)\text.
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