# Math Help - Continuity of a Piecewise Function

1. ## Continuity of a Piecewise Function

Let f: R->R be defined by
f(x)={x2 for x in Q, x+2 for x not in Q}

Find all points (if any) where f is continuous.

We learned that a function is continuous at a point where f(x)=limit as x->p f(x). I'm just not really sure how to go about finding these.

I think for all x in Q this function is discontinuous for all x not equal to zero, since that will be only case where f(x) will equal its limit. Is this correct thinking?

2. ## Re: Continuity of a Piecewise Function

Originally Posted by renolovexoxo
Let f: R->R be defined by
f(x)={x2 for x in Q, x+2 for x not in Q}
Find all points (if any) where f is continuous.
Is $f$ continuous at $x=2~?$

3. ## Re: Continuity of a Piecewise Function

f is continuous at the points satisfying x^2=x+2