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Modulus Function

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= max {x, –x}
Domain: R; Range: [0, ∞)
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Properties of modulus function

  1. |x| = a Points on the real number line whose distance from origin is a
     
    x = ±a
  2. |x| ≤ a x2a2 Points on the real number line whose distance from origin is a or less than a
     
    axa; (a ≥ 0)
  3. |x| ≥ a x2a2 Points on the real number line whose distance from origin is a or greater than a. x ≤ –a or xa; (a ≥ 0)
  4. a ≤ |x| ≤ b a2x2b2 x [–b, –a] [a, b]
  5. |x + y| = |x| + |y| x and y have same sign or at least one of x and y is zero or xy ≥ 0
  6. |x ± y| ≤ |x|+ |y|
  7. |x ± y| ≥ ||x| – |y||




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