In this exercise, we will use fixed-point iterations to find the real root of f(x) = 2x - x + 2x 1 = 0. To apply the fixed-point algorithm, we first need to rewrite Eq. (1) as x = representation is not unique. For example, we can write X = -2x + x +1 2 := 9(x), or X = 3 x - 2x + 1 2 := 9 (x). (1) g(x), but this In fact, the algorithm's convergence will depend on whether we choose 9 or 92 as our g(x). We will experiment with both versions, and you can use the Jupyter notebook 05-Nonlinear- eqs.ipynb for help. a) Find the expressions for g(x) and g (x) and, based on that, answer: would you rather select 9 or 92 as your g(x)? Why? b) (J) Set x(0) = 0.9 and g(x) = 9(x), and iterate until |x(+1) x(k)| < 10-6. What is the solution obtained, and how many iterations are needed to reach that? c) (J) Now, do the same for g(x) = 92(x). How many iterations are now needed?