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The function

$f(x)
= \begin{cases}
0 & \text{if x is rational}  \\
 x& \text{if x is irrational}  
\end{cases}$

is not continuous anywhere on the real line.
asked in Calculus by Veteran (30.3k points)   | 73 views

1 Answer

0 votes

False ;

It is continuous at x=0 since |f(x0)-0|<a for all a , whenever |x-x0|<a.

answered by (19 points)  


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