Let \( f:\mathbb{R} \longrightarrow \mathbb{R} \) defined by \( f(x)=\left\{\begin{matrix}
x^2 \, , \, &x \in \mathbb{R}\setminus \mathbb{Q} \\
x^3 \, , \, &x \in \mathbb{Q}
\end{matrix}\right. \)
a. Is \( f \) \( 1-1 \) ?
b. Determine the points at which the function is continuous.
c. Evaluate the derivative at the points at which the function is differentiable.
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