Question

Give the value of x where the function f(x)=(x^2-2x+1)/(x^2-1) has a removable discontinuity.

Answer 1

These discontinuity problems are giving me a lot of trouble.

Answer 2

I mean, I'm pretty sure I need to factor it out, which I've done. I end up with [(x-1)(x-1)]/[(x+1)(x-1)]. Then, after cancelling out (x-1) in the numerator and the denominator, I'm left with (x-1)/(x+1). But how do I use this information to determine what value of x will result in a removable discontinuity?

Answer 3

Thanks, I'm just hoping to learn the more precise way.

Answer 4

Well the values for which the function is undefined is when the denominator = 0
So x=/=-1

Answer 5

So I just read this.
In the original function, if you plug in x=1 or x=-1, then it is undefined.
The difference is that after you simplify it, plugging in a removable x will yield a nonzero answer

Answer 6

Meaning that your x=1 is removable

Answer 7

The answer is actually 1. I'm just trying to figure out how they arrived at that answer.

Answer 8

Ohh, lemme read that again.

Answer 9

Sorry its not very nicely phrased. you can look up the website I was reading off: http://integralcalc.com/removable-discontinuity-example-1/

Answer 10

Thanks, that vid is pretty helpful.

Answer 11

Np I learnt something new too