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Let $f:R\rightarrow R$ be defined as
$f(x)=\left\{\begin{array}{lr}0, & x \text { is irrational} \\ \sin |x|, & x \text { is rational }\end{array}\right.$ Then, which of the following is true?
Options:
$f(x)=\left\{\begin{array}{lr}0, & x \text { is irrational} \\ \sin |x|, & x \text { is rational }\end{array}\right.$ Then, which of the following is true?
Solution:
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Verified Answer
The correct answer is:
f is continuous at $x=k\pi$ where k is an integer
We have, $f(x)=\left\{\begin{array}{ll}0, & x \text { is irrational } \\ \sin |x|, x \text { is rational }\end{array}\right.$
If $f(x)$ is continuous, then $\sin |x|=0$ $\Rightarrow x=k \pi,$ where $k$ is an integer.
If $f(x)$ is continuous, then $\sin |x|=0$ $\Rightarrow x=k \pi,$ where $k$ is an integer.
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