Homework - Composite Functions

# Exercise 2 the price of gas started out at 100gallon

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• apiccirello
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Exercise 2 The price of gas started out at 100¢/gallon on the 1st of the month. Every day since then, it has gone up 2¢/gallon. My car takes 10 gallons of gas. (As you might have guessed, these numbers are all fictional.) Let d equal the date (so the 1st of the month is 1, and so on). Let g equal the price of a gallon of gas, in cents. Let c equal the total price required to fill up my car, in cents. a. Write a function g (d) that gives the price of gas on any given day of the month. b. Write a function c (g) that tells how much money it takes to fill up my car, as a function of the price of a gallon of gas. c. Write a composite function c (g (d)) that gives the cost of filling up my car on any given day of the month. d. How much money does it take to fill up my car on the 11th of the month? First, translate this question into function notation, and then solve it for a number. e. On what day does it cost 1,040¢ (otherwise known as \$10.40) to fill up my car? First, translate this question into function notation, and then solve it for a number.

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Exercise 3 Make up a problem like numbers 1 and 2. Be sure to take all the right steps: define the scenario, define your variables clearly, and then show the (composite) functions that relate the variables. Exercise 4 Find f (g (x)) if… a. g (x) = 3 b. g (x) = y c. g (x) = oatmeal d. g (x) = e. g (x) = (x + 2) f. g(x) = Exercise 5 If h(x) = 4x and h(i(x)) = x. Can you find what function i (x) is, to make this happen?
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