(10 points) Consider the following Fixed-Point iteration (FPI) functions x + 4 2r (A) g(x)= =...

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(10 points) Consider the following Fixed-Point iteration (FPI) functions x² + 4 2r (A) g(x)= = 1² +6 5 (B) g(x) = in the interval [1,3]. (a) Show that both FPI iteration functions converge to the unique fixed point r = 2. (b) Use the FPI method for each iteration function to find the root to within 10-6 using an initial guess as zo = 2.2. (c) Discuss the rate of convergence observed for each iteration function. Clearly explain your thinking. (10 points) Consider the following Fixed-Point iteration (FPI) functions x² + 4 2r (A) g(x)= = 1² +6 5 (B) g(x) = in the interval [1,3]. (a) Show that both FPI iteration functions converge to the unique fixed point r = 2. (b) Use the FPI method for each iteration function to find the root to within 10-6 using an initial guess as zo = 2.2. (c) Discuss the rate of convergence observed for each iteration function. Clearly explain your thinking.