# Thread: Values of A and B

1. ## 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"?

2. 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

3. ## ok

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

4. 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.

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

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

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

5. ## ok

I have not been able to find A and B.

Sorry....

6. 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:
$\displaystyle f(x) = \frac{x - B}{x - A}$

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

7. Originally Posted by blueridge
I have not been able to find A and B.

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

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

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

$\displaystyle 1 - A = 0$

$\displaystyle \Rightarrow A = 1$