Question

For every event he works, John's Catering charges a set-up fee of $120, plus $10 per person. a. Write a function c(p) to represent this situation. b. What are the domain and range of the function? c. What would the domain and range of the inverse of this function be? 3. Determine if the following are inverses and explain: a. f(x) = 5x – 10 g(x) = 1/5 x + 2 b. A

Answer 1

a. The function c(p) to represent this situation is: c(p) = 120 + 10p. b. The domain of the function is any positive integer since you can't have a negative or fractional number of people. The range of the function is any positive integer since the cost cannot be negative. c. The domain of the inverse function is any positive integer, and the range is any positive integer as well. d. The given functions f(x) = 5x – 10 and g(x) = 1/5 x + 2 are not inverses.

Step-by-step explanation:

a. The function c(p) to represent this situation is:
c(p) = 120 + 10p

b. The domain of the function is the set of all possible values for p, which represents the number of people. It would be any positive integer since you can't have a negative or fractional number of people. The range of the function is the set of all possible costs, which would be any positive integer since the cost cannot be negative.

c. The domain of the inverse function would be the set of all possible costs, which would be any positive integer. The range of the inverse function would be the set of all possible values for p, which represents the number of people, and it would be any positive integer as well.

3. The given functions f(x) = 5x – 10 and g(x) = 1/5 x + 2 are not inverses of each other. To check for inverses, we can substitute g(x) into f(x) and g(f(x)) should equal x, and vice versa. However, substituting g(x) into f(x) results in a different expression that does not simplify to x. Therefore, f(x) and g(x) are not inverses.