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Math Help - Values of A and B

  1. #1
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    Values of A and B

    If f(x) = (x - B)/(x - A), f(2) = 0 and f(1) is undefined, what are the avlue of A and B?

    Does the term "undefined" mean the same as "does not exist"?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by blueridge View Post
    If f(x) = (x - B)/(x - A), f(2) = 0 and f(1) is undefined, what are the avlue of A and B?
    I had the solution here, but i realize that you dont want answers.

    Hint: A fraction is zero if the numerator is zero (given its denominator is not zero at the same time), a fraction is undefined if the denominator is zero.


    Does the term "undefined" mean the same as "does not exist"?
    not really, but kind of. "undefined" means we can't assign a particular value to the expression, while "does not exist" means it's not there at all
    Last edited by Jhevon; June 11th 2007 at 01:15 PM.
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  3. #3
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    ok

    Can you show me step by step what to do leading to the correct answer?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by blueridge View Post
    If f(x) = (x - B)/(x - A), f(2) = 0 and f(1) is undefined, what are the avlue of A and B?

    Does the term "undefined" mean the same as "does not exist"?
    let me give you one more hint. see below, and then see the post i made before and see if you can figure it out, if not, i'll do a full solution.


    f(x) = \frac {x - B}{x - A}

    \Rightarrow f(2) = \frac {2 - B}{2 - A}

    \Rightarrow f(1) = \frac {1 - B}{1 - A}
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  5. #5
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    ok

    I have not been able to find A and B.

    Sorry....
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    Quote Originally Posted by blueridge View Post
    I have not been able to find A and B.

    Sorry....
    Well there is only one value of A that will make f(1) undefined:
    f(x) = \frac{x - B}{x - A}

    If the denomintator is 0 then the expression is undefined.

    So set x - A = 0 when x = 1.

    Thus
    1 - A = 0 ==> A = 1.

    So the expression is
    f(x) = \frac{x - B}{x - 1}

    We also know that f(2) = 0. The expression is 0 when the numerator is 0. So set x - B = 0 when x = 2.

    Thus
    2 - B = 0 ==> B = 2.

    So the expression is
    f(x) = \frac{x - 2}{x - 1}

    -Dan
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by blueridge View Post
    I have not been able to find A and B.

    Sorry....
    f(x) = \frac {x - B}{x - A}

    \Rightarrow f(2) = \frac {2 - B}{2 - A}

    Now we are told that f(2) = 0.

    \Rightarrow \frac {2 - B}{2 - A} = 0

    I also told you that a fraction is zero if the numerator is zero (provided the denominator isn't zero at the same time)

    so this means 2 - B = 0

    \Rightarrow B = 2


    Now f(1) = \frac {1 - B}{1 - A} and we are told this is undefined. i told you a fraction is undefined if we divide by zero. so this means

    1 - A = 0

    \Rightarrow A = 1
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