Use algebraic manipulation to show that each of the following functions has a fixed point at p

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Use algebraic manipulation to show that each of the following functions has a fixed point at p precisely when f (p) = 0, where f (x) = x4 + 2x2 − x − 3.
a. g1(x) = (3 + x − 2x2)1/4
b. g2(x) = (x + 3 − x4/2)1/2
c. g3(x) = (x + 3)/(x2 + 2)1/2
d. g4(x) = (3x4 + 2x2 + 3)/(4x3 + 4x - 1)
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Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

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