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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- Jun 11th 2007, 12:52 PMblueridgeValues 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"? - Jun 11th 2007, 01:02 PMJhevon
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.

Quote:

Does the term "undefined" mean the same as "does not exist"?

- Jun 11th 2007, 03:58 PMblueridgeok
Can you show me step by step what to do leading to the correct answer?

- Jun 11th 2007, 04:09 PMJhevon
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.

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

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

$\displaystyle \Rightarrow f(1) = \frac {1 - B}{1 - A}$ - Jun 11th 2007, 04:43 PMblueridgeok
I have not been able to find A and B.

Sorry.... - Jun 11th 2007, 04:47 PMtopsquark
Well there is only one value of A that will make f(1) undefined:

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

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

$\displaystyle f(x) = \frac{x - B}{x - 1}$

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

$\displaystyle f(x) = \frac{x - 2}{x - 1}$

-Dan - Jun 11th 2007, 04:51 PMJhevon
$\displaystyle f(x) = \frac {x - B}{x - A}$

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

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

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

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 $\displaystyle 2 - B = 0$

$\displaystyle \Rightarrow B = 2 $

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

$\displaystyle 1 - A = 0$

$\displaystyle \Rightarrow A = 1$