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Plot[Piecewise[{{Sqrt[2 - x^2/2], x < 2}, {Sqrt[(-4 + x^2)/(-2 + x^2)], x > 2}}], {x, 0, 4}]
Plot[Piecewise[{{Sqrt[2 - x^2/2], x < 2}, {Sqrt[(-4 + x^2)/(-2 + x^2)], x > 2}}], {x, 0, 4}]
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