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Why is the function f:R R defined by f(x) = sqrt(x^2) not valid? Some elements in the domain do not map to an element in

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Why is the function f:R R defined by f(x) = sqrt(x^2) not valid? Some elements in the domain do not map to an element in the target. Some elements in the domain map to more than one element in the target. This function is well-defined

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