Instructions: You are encouraged to work with other people from this class on this worksheet, but you must turn in your own worksheet by the due date at 11:59pm on Gradescope. When you submit your work to Gradescope, be sure to clearly 1 early label your questions. Each part of a question is worth one point unless otherwise indicated. SHOW ALL YOUR WORK Question 1: The volume of a sphere (in cm') can be expressed as a function of the radius of the sphere (in cm) as follows: V = f(r) = 4mr3. (a) Verbally interpret what f-1(100) means physically (not algebraically). Recall that alrebraically this means f(r) = 100 for some r. (b) Find the value of f-1(100). Include units. (c) Does f(r) have an inverse function? If so, find f-1(V). If not, why not? (d) Suppose the radius of the sphere is increasing at 2 cm per minute, t minutes after noon today. Let g(t) define the function whose input is the time (in minutes) since noon today and whose output is the radius of the sphere (in cm). Find g(t). (e) In the context of this question, does f(g(t)) make sense? If so, what does it mean? Does g(f (r)) make sense? If so, what does it mean