Question

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

• A. $f\left(x\right)$ is continuous at every $x$, except $x=0$
• B. $f\left(x\right)$ is discontinuous at every $x$, except $x=0$
• C. $f\left(x\right)$ is continuous everywhere
• D. $f\left(x\right)$ is discontinuous everywhere

Answer 1

The correct option is C $f\left(x\right)$ is continuous everywhere

Solution :-

f is defined in [5,5]

or domain has singleton element $\left\{5\right\}$

so f is every where Continuous

so option C is correct.