Let f be defined on [-5,5] as f(x)= l x if x is rational -x if x … - Vidyadip

MCQ

Let $f$ be defined on $[-5,5]$ as $ f(x)=\left\{\begin{array}{l} x \text { if } x \text { is rational } \\ -x \text { if } x \text { is irrational } \end{array}\right. $ Then $f(x)$ is

A
continuous at every $x$ except $x=0$
B
discontinuous at every $x$ except $x=0$
C
continuous everywhere
✓
discontinuous everywhere

✓

Answer

Correct option: D.

discontinuous everywhere

As $x \rightarrow 0$ both $x$ and $-x$ tend to zero, $f(0)=0$
$\therefore f(x)$ is continuous at $x=0$.
For $x \neq 0, x \neq-x,$
$f(x)$ is discontinuous.

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