# Continuous Function

1. Sep 24, 2009

### Loppyfoot

1. The problem statement, all variables and given/known data
For what positive values of b is f continuous for all real numbers x?
f(x) = ((x-1)(x2-4))/(x2-b)

So I go one value of b for the function to be continuous. I got that b=4. How do I find any others? If there even are any others?

Last edited: Sep 24, 2009
2. Sep 24, 2009

### LCKurtz

I suppose you mean "a", not "b". And no, if a = 4 it isn't continuous for all values of x because then it is an undefined 0/0 form when x = ±2. And if you cancel the offending factors it is no longer the same function.

3. Sep 24, 2009

### Loppyfoot

But when b=4, the top x^2-4 and the bottom x^2-4 cancel out to leave x-1.

4. Sep 24, 2009

### LCKurtz

Yes, but they are no longer the same function since they don't have the same domain. For example consider the function y = x/x. This is not defined when x = 0, so its domain is x ≠ 0. But if you cancel the x's you have y = 1 which is defined for all x. The two functions do not have the same domain so they are not the same function.

5. Sep 24, 2009

### Loppyfoot

So are there any values of b that make this function continuous?

6. Sep 24, 2009

### LCKurtz

I think you know the answer. You would need a positive b (positive was given) so (x2-b) never gives you a zero in the denominator for any x, eh?

7. Sep 24, 2009

### Loppyfoot

So there are no values of b that makes this function continuous?

8. Sep 24, 2009

### LCKurtz

That makes it continuous for all x, which is what was required.

9. Sep 24, 2009

### Loppyfoot

Alright, thanks LC!