GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
64 views
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 (29.2k points)   | 64 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)  


Top Users Apr 2017
  1. akash.dinkar12

    3508 Points

  2. Divya Bharti

    2542 Points

  3. Deepthi_ts

    2040 Points

  4. rude

    1966 Points

  5. Tesla!

    1768 Points

  6. Shubham Sharma 2

    1610 Points

  7. Debashish Deka

    1588 Points

  8. Arunav Khare

    1454 Points

  9. Kapil

    1424 Points

  10. Arjun

    1420 Points

Monthly Topper: Rs. 500 gift card

22,076 questions
28,040 answers
63,230 comments
24,135 users