Function Not Defined at x = 2

[turophile]

My textbook gives a function and says is it not defined at x = 2.

The function is: f(x) = (x - 2) (x[sup:2wg07ahh]2[/sup:2wg07ahh] - 1) sqrt(x)

Now I can see how the function would not be defined if the (x - 2) term were in the denominator of a fraction, but I can't see how it is undefined as given. Either something escapes me or there's a misprint in my textbook. Thanks for any pointers.

 

[Deleted member 4993]

My textbook gives a function and says is it not defined at x = 2.

The function is: f(x) = (x - 2) (x[sup:1ypjn9p2]2[/sup:1ypjn9p2] - 1) sqrt(x)

Now I can see how the function would not be defined if the (x - 2) term were in the denominator of a fraction, but I can't see how it is undefined as given. Either something escapes me or there's a misprint in my textbook. Thanks for any pointers.

If you have posted the problem correctly, then the function is not defined at x<0.

 

[turophile]

I double checked, and I did post the function as it's given in my textbook. I'll assume it is an error. Thanks!

 

[BigGlenntheHeavy]

\(\displaystyle f(x) \ = \ (x-2)(x^2-1)\sqrt x \ and \ is \ undefined \ at \ x \ = \ 2, \ has \ a \ removable \ discontinuity \ at \ x \ = \ 2.\)

\(\displaystyle Hence, \ \lim_{x\to2}f(x) \ = \ 0 \ and \ domain \ of \ f(x) \ is \ [0,2)U(2,\infty)\)

\(\displaystyle See \ graph \ below, \ note \ at \ x \ = \ 2, \ imagine \ a \ hole.\)

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