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

Question 3 (a) Define the function f : R - R by 8 f ( x ) = if x * 2, x - 2 4, 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 x2 - 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 R. Given that f' (2022) = 1, find the value of f'(-2022). (7 marks)

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