# A function that is not?

Calculus Level 5

$f(x) = \begin{cases} \sin x & \text{for } x \in \mathbb{Q} \\ (\ln x)^2 & \text{for } x \notin \mathbb{Q} \end{cases}$

Consider the function $$f$$ defined over the set of positive real numbers.

Which of the following statements about the function $$f$$ is true? 

Notations:

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