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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
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 $x=0$
  • ✓
    discontinuous at every $x$ except $x=0$
  • C
    continuous everywhere
  • D
    discontinuous everywhere
✓

Answer

Correct option: B.
discontinuous at every $x$ except $x=0$
(b) : 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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