Question: If = f() but the iteration x n+1 = f (x n ) fails to converge to the root a, under what condition on

If α = f(α) but the iteration x_n+1 = f (x_n) fails to converge to the root a, under what condition on f(x) will the iteration x_n+1 = f⁻¹(x_n) converge?

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