5. Function over a continuous set. (10 points) Consider the function 1 forzcgl, 91(15): % for1

5. Function over a continuous set. (10 points) Consider the function 1 for x < 1, for 1 < x < 5, 0 for x > 5. (a) What is the domain and range of this function? (b) What is the image of each of the sets: (i) [2, 3], (ii) (00, 3], and (iii) [4, 00) under (c) What is the inverse image of the sets: 00, 0.5], (ii) ( 00, 0], and (iii) [0.5, 00) under g? Hint: In answering parts (b) and (c), it may be helpful to sketch the function.