Question

find the discontinuities if there are any. which of the discontinuities are removable?
1) f(x)=x^2-2x+1
2) f(x)= (1) / (x^2+1)
3) f(x)= (1) / (x-1)

Answer 1

i don't really know what to do. do i plug in a number for each x?

Answer 2

You are looking for any values of x for which the function is undefined which means having a 0 in the denominator.

Answer 3

The first function is continuous since there is no undefined x for the function. The function is defined for all values of x.

Answer 4

Skip to #3 for the moment. Can you identify any value of x for which the denominator is 0?

Answer 5

@qtexpress101, you'll need to communicate with your helper

Answer 6

sorry i had to step away for a moment. the door rang

Answer 7

Also, a removable discontinuity is a single-point "hole" in the function. If the discontinuity can be filled by one point, it is called removable.

Answer 8

for #3, its 1

Answer 9

what if it doesn't have a denominator? like the first example

Answer 10

That's good! You are getting this. And since it is a single point, it is removable.

Answer 11

I brought up possible zeros in the denominator because your examples were like that. You can have other types of discontinuities like undefined square roots.

Answer 12

I'll give an example f(x) = sqrt(x) is undefined for all x < 0. That's more than just one point, it's actually infinite, so that type of discontinuity is not removable.

Answer 13

my book mentions that #3 is a non removable discontinuity at x =1

Answer 14

Actually, you're right. The limit as x approaches that value has to exist. Here, the limit is infinity, so the discontinuity is not removable.

Answer 15

so how can i get for #2, a 0 in the denominator? anything negative will just turn even

Answer 16

in that case will it be continuous for all real x?

Answer 17

You can't because x^2 is always greater than or equal to 0, so the denominator will be at least 1.

Answer 18

Yes, that function will be continuous for all x.

Answer 19

ok i get ya now, thanks!

Answer 20

so, 1 and 2 will be continuous with 3 discontinuos at 1 (not removable). and thx for the medal.

Answer 21

:D

Answer 22

so f(x)= (x)/(x^2-1) would be a removable discontinuity at x = 1?