Precalculus Activity: Compositions Purpose: To investigate another way to combine functions and in particular to observe what happens when we combine a function with its inverse in this way. Procedure: Work on this activity in groups of size 2 to 3. 1. A therapeutic drug has the side effect of raising a patient's heart rate. The relationship between Q, the amount of the drug in the patient's body (in milligrams), and r, the patient's heart rate (in beats per minute) is given by r(Q) = 60 + 0.2Q. Over time the level of the drug in the patient's bloodstream changes. The amount of drug in the patient's body, Q, (in milligrams) t minutes after the drug has been administered is given by Q (t) - 250(0.8). a. What is the heart rate of this patient 5 minutes after the drug was administered? 8 minutes? 10 minutes? 13 minutes? b. Explain the process that you are using to answer (a). c. Represent symbolically how the heart rate of this patient is changing over time. d. Definition - Composition of functions: For two functions, f and g, we can define a new function, called the composition of f and g (denoted by f . g), by using the output of one function as the input for the other. This leads to the following definitions: (f .g)(x) =f(g(x)) and (g . f) (x) =g(f(x))