4. Let f(x) = 2 - 1 (a) Consider computing f(x) via the following algorithm: = 1: y = e^x 2: return y - 1 Is this algorithm stable? Justify your answer (b) Let x have the value 9.999999995000000 x 10-10, in which case f(x) is equal to 10-9 up to 16 decimal places. How many correct digits does the algorithm listed above give you? Is this expected? (c) Find a polynomial approximation of f(x) that is accurate to 16 digits for all |z|