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

Recall that the absolute value |x| for a real number x is defined 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 to 0.
(d) −|x| ≤ x ≤ |x|.

Expert Solution

Colby Messinger answered 2 years ago

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