If $f(x) = 2a - x$ for $x < a$ and $f(x) = 3x - 2a$ for $a \leq x$, then which of the following is true?

Question

$f(x)$ is discontinuous at $x = a$

$f(x)$ is not differentiable at $x = a$

$f(x)$ is differentiable at all $x \geq a$

$f(x)$ is continuous at all $x$

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