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Math Help - Find the domain of f(x) = ln(x+1)

  1. #1
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    Find the domain of f(x) = ln(x+1)

    Please help, I looked in my book to find an explanation for this and found nothing that made sense.

    How do I begin to find the domain for:

    f(x) = ln(x+1)


    Please provide steps (if possible), Thanks!
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by lilrhino View Post
    Please help, I looked in my book to find an explanation for this and found nothing that made sense.

    How do I begin to find the domain for:

    f(x) = ln(x+1)


    Please provide steps (if possible), Thanks!
    Step one: What values of x can we plug into the equation and still get a solution? Included with this question is: What values of x can we not plug into the equation to get a solution?

    Since the function is log, we know that we cannot take the log (ln in this case) of a negative number or of 0, so the term inside the function must be >0.

    Step two: Find these values of x.

    The term inside the log is (x + 1), so:
    (x + 1) > 0
    x > -1

    That is your domain, which can be written as:
    D = (-1,inf)
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  3. #3
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    Quote Originally Posted by ecMathGeek View Post
    Step one: What values of x can we plug into the equation and still get a solution? Included with this question is: What values of x can we not plug into the equation to get a solution?

    Since the function is log, we know that we cannot take the log (ln in this case) of a negative number or of 0, so the term inside the function must be >0.

    Step two: Find these values of x.

    The term inside the log is (x + 1), so:
    (x + 1) > 0
    x > -1

    That is your domain, which can be written as:
    D = (-1,inf)
    Since we can plug an infinite amount of numbers in - I guess that's where we get our infinity portion of the answer.

    But, how do you determine how you actually write out the answer? Is it because you begin with -1 and end with an infinite amount of solutions?

    I'll have to memorize the rule that we can't take the log of 0 or a negative number so that's how we get the (x + 1) > 0

    Thank you so much for your response
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  4. #4
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by lilrhino View Post
    Since we can plug an infinite amount of numbers in - I guess that's where we get our infinity portion of the answer.

    But, how do you determine how you actually write out the answer? Is it because you begin with -1 and end with an infinite amount of solutions?

    I'll have to memorize the rule that we can't take the log of 0 or a negative number so that's how we get the (x + 1) > 0

    Thank you so much for your response
    When I said that the domain is x > -1, this indicates that x is all real numbers greater than -1. We can denote this by saying that x "is all values from -1 to infinity, not including infinity or -1" which we write as (-1,inf).

    If, for example, the domain was x < 10, the domain would be "all values less than 10" which is "all numbers from negative infinity to 10," which can be written as (-inf,10).
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