1

A question defines an f(x) that is x when x is rational and 1-x when x is irrational, and asks for the points where the function is continuous. The answer equates the two expressions and says the answer's $\frac{1}{2}$.

Why is this so? I can only think of the graph being nearly a combination of $y=x$ and $y=1-x$. How does the intersection point give the point of continuity?

harry
  • 1,076
  • 1
    Take any point $c$ and see what the limit of $f(x)$ as $x \to c$ through rational numbers and the limit of $f(x)$ as $x \to c$ through irrational numbers are. For continuity these two limits have to be the same. – Kavi Rama Murthy Nov 08 '20 at 08:23
  • This solves it, can you post it as an answer? – harry Nov 08 '20 at 08:28

0 Answers0