Decide Whether the Given Function Has an Inverse

question 55

Essay

Decide whether the given function has an inverse. Defend your decision.

(a) P (x) is the cost, in cents, of mailing a letter that weighs x ounces.

(b) C (t) is the total number of cars which have driven past a particular point along a highway during a specific day where t represents the time, in hours, since midnight.

(c) F (d) is the amount of fuel, in gallons, in your car when you have traveled d miles on a particular tankful of gas.

(d) S (t) is the number of shoppers entering the Mall of America where t is the number of minutes past midnight on one particular day.

(e) T (t) is the temperature inside an oven where t is the time, in minutes, from the beginning to the end of the oven's self-cleaning cycle.

(f) V (x) is the volume of a cube whose side has length x.

(g) f (n) is the number of students enrolled in your calculus class on the nth day of the term.

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Definitions:

JIT

Just-in-Time is a management strategy that aligns raw-material orders from suppliers directly with production schedules.

Distribution Systems

Networks and processes involved in moving a product from the supplier to the customer, including logistics, warehousing, and retailing.

U.S. Coal

Coal mined in the United States, a key natural resource used for electricity generation and manufacturing processes.