a) By considering suitable transformations, sketch by hand the graph of the function g(x) = 3 + 2 sin 2x for 2 x 2. [3] (b) Write down the image set of g, giving your answer in interval notation. [1] (c) This part of the question concerns the function h(x) = 3 + 2 sin 2x for k x k By considering your graph from (a), or otherwise, state the largest value k can take if h(x) is to be a one-to-one function. [1] (d) Using your answer to (c), obtain the inverse function of h(x) and state its domain and image set.