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

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.

(See attached file for full problem description with proper equations)
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3. Let T(x) = x^2 Show that T is a contraction on (0, 1/3] , but that T has no fixedpoint on this interval. Does this conflict Theorem 6.4? Explain.
Note: We are using the book Methods of Real Analysis by Richard R. Goldberg.
This

A manufacturer finds that the cost y of producing x units is given by the formula of the form y=mx+b. If it costs $1300 to produce 20 units and $1750 to produce 35 units, what is the fixed cost?

A number (a) is called a fixedpoint of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixedpoint.

FixedPoint iteration method.
Use a fixed-point iteration method to find an approximation to that is accurate within 10-4
See attached file for full problem description.

Let f be a continuous function on the closed interval [0,1] with range also contained in [0,1].Prove that f must have a fixedpoint; that is, show f(x)=x for at least one value of x belong to [0,1].

Part a)
Given the following predator prey model where x(t) is the predator population and y(t) is the prey population:
dx/dt = - ax + bxy + (z1)*x
dy/dt = cy - gxy +(z2)*y
Here both z1 and z2 can be positive or negative; parameters a, b, c, g are all defined to be positive.
Parameters z1 and z2 can r

1. The equation x - 3 ln x = 2 has exactly two solutions A and B, with 0 < A < B.
(You do not have to show this.)
(a) Show that A is in [0.5,0.7], and B is in [8.3,8.5].
(b) Consider the following fixed-point iteration for finding a solution of the given
equation: xn+1 = e(1/3(Xn-2)):
Show that if X0 = B+ E, where E is

Hello, I am learning algebra 2. I have no help and the textbook gives very few and vague examples. Can someone help me with my algebra 2 work.
1.Find all solutions for the following system of equations. List the solutions as ordered pairs. {x^2+y^2-25 = 0
2x-y = -5
2.Solve the system of linea