Question: Question 3 (a) Define the function f: R - R by x3 - 8 f (x) = if x # 2, x - 2 if

Question 3 (a) Define the function f: R - R by x3 - 8 f (x) = if x # 2, x - 2 if x = 2. Discuss the continuity of the function f (x) at x = 2. Explain your answer. (6 marks) (b) Define the function g: R - R by x - c2 g (x) = if x # c, x - C CX, if x = c. Discuss the continuity of the function g(x). For which values of c is the function g(x) continuous? Explain your answer. (7 marks) (c) Let f be a differentiable function such that f (-x) = f (x) for all x E . Given that f' (2022) = 1, find the value of f'(-2022). (7 marks)

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