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g(x)=1+1+x1. (a) Show that g maps the interval [1,2] into the same interval [1,2], which means to show that 1g(x)2, for all x[1,2]. (b) Find a theorem, or part of a theorem from the book (or the class notebook) concluding that g has at least one fixed point in the interval [1,2]. Give the theorem number, theorem part (Part (i), or (ii), or ...) and book's edition (or show how to find it in the notebook) or simply state the part that matters to this question. And, clearly indicate how the hypotheses of that theorem are met. (Hint: g is continuous everywhere, except at x=1.) (c) Find the best possible value of k, such that g(x)k, for all x[1,2]. Show your reasoning clearly. (d) Find a theorem, or part of a theorem from the book (or the class notebook) concluding that g has exactly one fixed point in the interval [1,2]. Give the theorem number, theorem part (Part (i), or (ii), or ....) and book's edition (or show how to find it in the notebook) or simply state the part that matters to this question. And, clearly indicate how the hypotheses of that theorem are met. (Hint: Does g exist on the interval? Is k