SOLUTION: Need help with a problem. If f(x)=(x-B)/(x-A), f(-3)=0, and f(5) is undefined, what are the values of A and B?

Algebra ->  Matrices-and-determiminant -> SOLUTION: Need help with a problem. If f(x)=(x-B)/(x-A), f(-3)=0, and f(5) is undefined, what are the values of A and B?      Log On


   

Question 966110: Need help with a problem. If f(x)=(x-B)/(x-A), f(-3)=0, and f(5) is undefined, what are the values of A and B?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x-A=0 will be 0 if A=-x, or x=-A, and f(x) will be undefined at x=-A.
MEANING: Your denominator is x-5.

x-B=0 means that x=B. You wanted -3-B=0, because that is according to f%28-3%29=0, a zero or root of the function.
-
-3-B=0
-3=B
The numerator is x-%28-3%29=x%2B3.

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!

1) The fact that  f(5)  is undefined means that  A=5.  This is the only value when the function  %28x-B%29%2F%28x-A%29  is undefined.

      So,  your function is  f(x) = %28x-B%29%2F%28x-5%29.

2) Now use the equation  f(-3) = 0.

      It means that  %28x-B%29%2F%28x-5%29 = 0  at  x= -3.

      In turn, its means that  x-B =0  at  x= -3.

      In other words,  -3-B = 0.

      Hence,  B = -3.

Answer.  A = 5,  B = -3.