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TIFR-2013-Maths-C: 29

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True/False Question :

Let $f$ be a function on the closed interval $\left [ 0,1 \right ]$defined by

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

                                   $f\left ( x \right )=x^{2}$    if $x$ is irrational

Then $f$ is continuous at $0$ and $1$.

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