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Math Help - A function to convert a +ve number to a number from 0 to 1

  1. #1
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    A function to convert a +ve number to a number from 0 to 1

    I need a mathematical function, which converts any positive number (from 0 to any large value) to a number in the range 0 to 1.
    Please help
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  2. #2
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    Quote Originally Posted by neerajraj1000 View Post
    I need a mathematical function, which converts any positive number (from 0 to any large value) to a number in the range 0 to 1.
    Please help
    f(x) = e^{-x}.
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  3. #3
    MHF Contributor ebaines's Avatar
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    Here's another:

    <br />
f(x) = \frac 1 {1 + x}<br />
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    Modified question

    Thank you for responding. Actually I need a function which should be monotonically increasing and converts any +ve number to a number within the range 0 to 1. (The function should use the whole range between 0 to 1. For example for 1/(1+x) as the value of x increase, the function gives less value, I want the opposite).
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  5. #5
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    if f(x) is monotonically decreasing and gives answers in the range (0,1)

    then 1-f(x) is monotonically increasing and gives answers in the range (0,1)


    So you could use: 1- \frac{1}{1+x} if you want a monotonically increasing version. (This simplifies to \frac {x}{1+x})

    or indeed
    1- e^{-x}
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  6. #6
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    Quote Originally Posted by neerajraj1000 View Post
    Thank you for responding. Actually I need a function which should be monotonically increasing and converts any +ve number to a number within the range 0 to 1. (The function should use the whole range between 0 to 1. For example for 1/(1+x) as the value of x increase, the function gives less value, I want the opposite).
    Then \frac{x}{x+1}. That is an increasing function and maps [0, \infty) into [0, 1).

    If, by "The function should use the whole range between 0 and 1." you mean that the function should have both the values 0 and 1, as well as all values between, for some finite, x, that is impossible for an increasing function on [0, \infty).
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