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Math Help - B = A + (n/(b+1))*(1-A) Please check if this function is mathematically sound

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    B = A + (n/(b+1))*(1-A) Please check if this function is mathematically sound

    Hi, everyone, this is my first post. I just need help regarding a function. Here it goes:
    I am using a function: B = A + (n/(b+1))*(1-A) ---- (I)
    where n = 1 - e^(-x) i.e. a monotonically increasing function with the value of x (where x will have a minimum value of 0 or any positive value) in the range 0 to 1
    and b has a minimum value of greater than or equal to zero.
    Question: My query is : 1. Is (I) a mathematically sound equation.
    2. Moreover, when n/(1+b) = 1 then b = n - 1
    Now if n = 0 then b = -1 (But how this is possible, as b has a minimum value of 0).

    3. Please check this equation for all boundary values for n and b, and me know if this function is mathematically fine or should I change this.
    PLEASE HELP.
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    Re: B = A + (n/(b+1))*(1-A) Please check if this function is mathematically sound

    Quote Originally Posted by priyahya100 View Post
    Hi, everyone, this is my first post. I just need help regarding a function. Here it goes:
    I am using a function: B = A + (n/(b+1))*(1-A) ---- (I)
    where n = 1 - e^(-x) i.e. a monotonically increasing function with the value of x (where x will have a minimum value of 0 or any positive value) in the range 0 to 1
    and b has a minimum value of greater than or equal to zero.
    Question: My query is : 1. Is (I) a mathematically sound equation.
    What do you mean by "mathematically sound"? B certainly is a function of the three variables A, b, and x or a function of any one with the other two as variables.

    2. Moreover, when n/(1+b) = 1 then b = n - 1
    Now if n = 0 then b = -1 (But how this is possible, as b has a minimum value of 0).
    If "n= 0", then n/(1+b)= 0, not 1, so "n/(1+ b)= 1 is wrong. Going back to your original equation, if n= 0, B= A and b can be any number from 0 to 1.

    3. Please check this equation for all boundary values for n and b, and me know if this function is mathematically fine or should I change this.
    PLEASE HELP.
    You say that b cannot be less than 0 so I guess 0 is a "boundary value" for b but I don't know what other boundary values you are talking about.
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