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"?
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.
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
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.
$\displaystyle f(x) = \frac {x - B}{x - A}$
$\displaystyle \Rightarrow f(2) = \frac {2 - B}{2 - A}$
$\displaystyle \Rightarrow f(1) = \frac {1 - B}{1 - A}$
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
$\displaystyle f(x) = \frac {x - B}{x - A}$
$\displaystyle \Rightarrow f(2) = \frac {2 - B}{2 - A}$
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
$\displaystyle 1 - A = 0$
$\displaystyle \Rightarrow A = 1$