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I am working on a function given as f(x) = 10/x + (1/20)x^2 for x such that 0≤x≤10. What can be said about the contraction mapping property of f(x)=x?

If it is not a contraction map, is there any way to make modifications on the function or the interval and prove a contraction mapping result? The upper bound in the interval is important to keep..

Attempt on problem: I can verify that |f'(x)|≤0.9<1 but I am stuck when it comes to showing that the function maps onto itself in the given interval. It is indeed not true since f(x)→infinity when T=0.

Thanks very much!!

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# Is this a contraction mapping?

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