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Absolute Values and Functions

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data
    I do not see how the two equations in each example are related, what should I do with them? (the l's are absolute value brackets):

    a) Let g(x) = 3x - 3 + l x+5 l. Find all values of a which satisfy the equation:

    g(a) = 2a +8

    b) Let h(x) = l x l - 3x + 4. Find all solutions to the equation :

    h(x - 1) = x - 2

    I know how to find an equation of the following:

    x + l 2x-1 l, find f(x) = 8

    x + l 2x-1 l = 8

    l 2x-1 l = 8-x

    2x-1 = 8-x or -2x+1= 8-x
    x=3 x=-7
  2. jcsd
  3. Jan 23, 2009 #2


    Staff: Mentor

    For part a, you have the formula for g(x), so g(a) = 3a -3 + |a + 3|

    Set that expression equal to 2a + 8. Isolate the absolute value expression on one side, and keep in mind that |x| = x if x >= 0 and |x| = -x if x < 0.
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