Confusion about continuity question.

[mathstudent79]

1.The Question

The function f(x)=


x²/x if (x≠0)



0 if(x=0)

The Attempt at a Solution

I thought this had a removable discontinuity at x=0, because the function s²/x is not defined at x=0, and the expression can be reduced to x.

The book (one of those AP prep guides with solutions) says that it is continuous everywhere, to note that x²/x if x≠0 and lim(x->0) f = 0.

Why was I wrong?

Thanks in advance.

 

[SammyS]

1.The Question

The function f(x)=

x²/x if (x≠0)

0 if(x=0)

The Attempt at a Solution

I thought this had a removable discontinuity at x=0, because the function s²/x is not defined at x=0, and the expression can be reduced to x.

The book (one of those AP prep guides with solutions) says that it is continuous everywhere, to note that x²/x if x≠0 and lim(x->0) f = 0.

Why was I wrong?

Thanks in advance.

The function g(x) = x²/x does have a removable discontinuity at x=0.

The piecewise function, f(x) that you give has that discontinuity removed. f(x) is defined for all x, and is continuous for all x, even for x = 0.

 

[mathstudent79]

SammyS

Thanks so much for your quick response.


So, just to be sure, once the discontinuity is removed, the function is continuous everywhere, is that right?

Thanks again.

 

[SammyS]

SammyS

Thanks so much for your quick response.


So, just to be sure, once the discontinuity is removed, the function is continuous everywhere, is that right?

Thanks again.

Yes, that's right.