Values of A and B

**blueridge** · June 11th 2007, 12:52 PM

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"?

**Jhevon** · June 11th 2007, 01:02 PM

Originally Posted by blueridge

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

**blueridge** · June 11th 2007, 03:58 PM

Can you show me step by step what to do leading to the correct answer?

**Jhevon** · June 11th 2007, 04:09 PM

Originally Posted by blueridge

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.

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

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

$\Rightarrow f(1) = \frac {1 - B}{1 - A}$

**blueridge** · June 11th 2007, 04:43 PM

I have not been able to find A and B.

Sorry....

**topsquark** · June 11th 2007, 04:47 PM

Originally Posted by blueridge

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

**Jhevon** · June 11th 2007, 04:51 PM

Originally Posted by blueridge

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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