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Let f(x) = x^(3) - x^(2) + x + 1 and g(x...

Let `f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):}` Then, g(x) in [0, 2] is

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continuous and differentiable on (0,2)-{1}
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