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Recall that the absolute value |x| for a real number x is defined as the function |x|...

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Advance Math

Recall that the absolute value |x| for a real number x isdefined as the function

|x| = x if x ? 0 or ?x if x < 0.
Prove that, for any real numbers x and y, we have
(a) | ? x| = |x|.
(b) |xy| = |x||y|.
(c) |x-1| = 1/|x|. Here we assume that x is not equal to0.
(d) ?|x| ? x ? |x|.

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