Explore BrainMass

Explore BrainMass

    Fixed Point Equations

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    The chapter in question is about Iteration.(x2 means x squared).
    It talks about the Fixed point rule. It describes a fixed opint equation as
    x2 + 1/8 = x; that is x2 - x + 1/8 = 0

    It then gives another example:
    Determine the fixed points of the function f(x) = -1/8x2 + 11/8x + 1/2
    and states that the fixed point equation is:

    -1/8x2 + 11/8x + 1/2 = x; that is, x2 - 3x - 4 =0
    I don't know how this has been achieved - I did try adding the x fractions and multiplying by 2 and then 1/2(-8) =4.

    Another example says:
    The fixed point equation is

    1/8x2 - x + 7 = x; that is, x2 - 16x +56 = 0

    Then finally:
    f(x) = -1/4x2 + 4/3x + 5/3

    The question says-use algebra to find the fixed points of f, which I assume to mean
    using a quadratic equation as above.
    I've tried adding the similar fractions and have come up with a possible answer

    x2 +12x + 20 = 0

    © BrainMass Inc. brainmass.com October 9, 2019, 7:50 pm ad1c9bdddf

    Solution Summary

    Fixed-point equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.