# Homework Help: Continuous Function Problems AP Calculus

1. Sep 21, 2009

### Loppyfoot

1. The problem statement, all variables and given/known data
Let f be the function given by f(x)= (x-1)(x²-4)/ (x²-a). For What Positive Values of a is f continuous for all real numbers x?

2. Relevant equations

3. The attempt at a solution
What I tried doing was separating the (x²-4) into (x+2)(x-2) then moving along from there, but I can't seem to figure out what number a can be without having a discontinuity.

Thanks for trying!
Loppyfoot

2. Sep 21, 2009

### LCKurtz

Hint:

1. Are polynomials continuous?
2. Are products of continuous functions continuous?
3. Are quotients of continuous continuous?

Are any of the answers above valid for all values of x or are any of them subject to some "if" conditions?

3. Sep 21, 2009

### Loppyfoot

So Then, I would guess a=4, because the the (x²-4) and the (x²-4) cancel out and you are left with (x-1).

4. Sep 21, 2009

### LCKurtz

You aren't permitted to cancel anything out since that makes minor changes in the function. Try answering the three questions I posed. That might lead you to the solution.

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