Find A and B?

Question

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

Answer 1

undefined means that there is an illegal operation like dividing by zero. the info given says that when you substitude 1 for x(f(1) the result is undefined. The only way it can happen is if the denominator equal zero.

(1-B) / (1-A) = undefined

so, A =1 because 1 - 1 = 0 . It will look like this.

(1-B) / (1-1) or (1-B)/0

it doesn't matter what B is because when you cannot divide by zero.

Ok now that we know what A is lets do the other case f(2) = 0
substituting we get

(2-B) / (2-1) we simplify and get (2-B) / 1 or (2-B).

ok so what number can you take away from 2 and get zero. Thats right 2. So B is 2. Just to make sure lets do the problem again but putting in the numbers for A and B. So the equation will look like this.

f(x)=(x-2)/(x-1)

now substitute the numbers again. f(1) = (1-2)/(1-1) or -1/0 undefined.

ok now case two. f(2) = (2-2)/(2-1) or 0/1 = 0.

Answer 2

f(1) undefined means that 1-A=0 , so A=1
f(2) =0 means that 2-B=0, so B=2