What are the conditions for cubic convergence in functional iteration?

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Homework Statement


Consider an iteration function of the form F(x) = x + f(x)g(x), where f(r) = 0 and f'(r) != 0. Find the precise conditions on the function g so that the method of functional iteration will converge cubically to r if started near r.

Homework Equations


I really don't know.



The Attempt at a Solution


I have no idea how to even begin!

Thanks in advance!
 
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DeadxBunny said:
I have no idea how to even begin!
Try starting with definitions.
 

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