1
$\begingroup$

Is $\frac{x-|x|}{x}$ continuous? It should be discontinuous at x=0 as left hand limit and right hand limit at zero are unequal. But it is continuous and the reason given is that they have excluded zero as its domain. Is it possible?

$\endgroup$
3
$\begingroup$

The function is continuous everywhere where it is defined. Speaking of continuity at $0$ makes no sense since the function is undefined at $0$.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Thank you very much. Can you clear one more doubt please? What is this concept called? Is this jump Discontinuity? $\endgroup$ – Elder Gate 1 Dec 29 '16 at 8:43
  • $\begingroup$ @user402626 What "concept" are you talking about? $\endgroup$ – 5xum Dec 29 '16 at 8:44
  • $\begingroup$ When right hand limit and left hand limit are unequal still the function is continuous...how? $\endgroup$ – Elder Gate 1 Dec 29 '16 at 8:45
  • $\begingroup$ @user402626 Well, the function is not continuous at $0$. It also isn't discontinuous at $0$. It's not defined at $0$, so talking about continuity at $0$ is like talking about what colour an invisible unicorn is. $\endgroup$ – 5xum Dec 29 '16 at 8:46
1
$\begingroup$

Hint: Let $f(x)=(x-|x|)/x$ for $x \ne 0$. Then

$f(x)=0$ for $x>0$ and $f(x)=2$ for $x<0$

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

Domain of given function is $x\in \mathbb{R} - \{0\}$

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.