in Calculus
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3 votes

The function f: \mathbb{R} \rightarrow \mathbb{R}  is defined as follows.

f(x) = \left\{\begin{matrix} 3x^2\ if \ x \in Q \\ -5x^2\ if \ x \notin Q \end{matrix}\right.

Which of the following is true?
(A) f is discontinuous at all
(B) f is continuous only at x = 0 and differentiable only at x = 0.
(C) f is continuous only at x=0 and non differentiable at all x \in \mathbb{R}
(D) f is continuous at all x \in \mathbb{Q} and non differentiable at all x \in \mathbb{R}

in Calculus
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