$f$ is defined in $\left[ { - 5,5} \right]$ as $f\left( x \right) = x$ if $x$ is rational $\,\,\,\,\,\,\,\,\,\,\,\,\,$ $ = - x$ if $x$ is irrational. Then

Question

$f$ is defined in $\left[ { - 5,5} \right]$ as

$f\left( x \right) = x$ if $x$ is rational

$\,\,\,\,\,\,\,\,\,\,\,\,\,$ $ = - x$ if $x$ is irrational. Then

$f(x)$ is continuous at every x, except $x = 0$

$f(x)$ is discontinuous at every $x,$ except $x = 0$

$f(x)$ is continuous everywhere

$f(x)$ is discontinuous everywhere

Solution

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