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Math Help - help with modulus function

  1. #1
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    help with modulus function

    I am studding modulus function at college. I don’t understand this part can you explain each of these please?
    І x – a І =x - a for x ≥ a and I x- a I = -( x – a ) = a-x for x<a
    I x – b I ≤ a ↔ - a ≤ x – b ≤ a
    І x – b I ≤ a ↔ - a + b ≤ x ≤ a +b
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  2. #2
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    Quote Originally Posted by mike789 View Post
    I am studding modulus function at college. I don’t understand this part can you explain each of these please?
    І x – a І =x - a for x ≥ a and I x- a I = -( x – a ) = a-x for x<a
    I x – b I ≤ a ↔ - a ≤ x – b ≤ a
    І x – b I ≤ a ↔ - a + b ≤ x ≤ a +b
    These are basic definitions of the modulus function.


    1. Remember that, by definition:

    |x| = x\textrm{ if }x > 0, 0 \textrm{ if }x = 0, -x \textrm{ if }x < 0.

    Now replace x with x - a.

    What happens to the resulting inequalities?



    2. It helps if you think of the modulus function as the "size" of whatever is inside it.

    So |x - b| \leq a is the same as saying

    "the size of x - b is never any more than a."

    It then follows that

    |x - b| \leq a is equivalent to -a \leq x - b \leq a.



    3. We saw from Q2 that

    |x - b| \leq a is the same as

    -a \leq x - b \leq a.


    Now add b to everything in the inequality. What happens?
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