f is defined on [-5,5] as f(x)=x if x is rational, =-x if x is irrational.

Question

$f$ is defined on $[-5,5]$ as $f(x)=x$ if $x$ is rational, $=-x$ if $x$ is irrational. Then

Accepted Answer

At a rational $a
e0$: $f(a)=a$ but $\displaystyle\lim_{x	o a}f(x)=-a$ (approaching through irrationals) --- discontinuous. Similarly for irrational $a
e0$. At $x=0$: both give $0$, so continuous there. Hence $f$ is discontinuous everywhere except $x=0$.

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