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Question 1. Consider these real-valued functions of two variables: T In (x2 + y2) (a) () What is ...

Question 1. Consider these real-valued functions of two variables: T In (x2 + y2) (a) () What is the maximal domain, D, for t

Question 1. Consider these real-valued functions of two variables: T In (x2 + y2) (a) () What is the maximal domain, D, for the functions f and g? Write D in set notation. (ii) What is the range of f and g? Is either function onto? ii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: z00, 2, 04 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding ▽g, on your diagram from (iv) mark the direction of ▽g(3,1). and Vg 2,0 20 40 (vi) Describe the symmetries of g(x, y)
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