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

Consider the function \(f\) defined over the set of positive real numbers.

Which of the following statements about the function \(f\) is true? \[\]

**Notations**:

\(\mathbb Q \) denotes the set of rational numbers.

\(\mathbb R \) denotes the set of real numbers.

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