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Let max $\{a, b\}$ denote the maximum of two real numbers $a$ and $b$. Which of the following statement(s) is/are $\text{TRUE}$ about the function $f(x) = \text{max}\{3 - x,x -1\}$?

  1. It is continuous on its domain.
  2. It has a local minimum at $x = 2$.
  3. It has a local maximum at $x = 2$.
  4. It is differentiable on its domain.
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