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:

Cytokines

Signaling molecules secreted by cells that have an effect on the behavior of cells, involved in immune responses, inflammation, and the healing process.

Cell-mediated Immune Response

The branch of the immune response that involves the activation of T-cells and the direct destruction of infected cells.

T cells

A type of lymphocyte developed in the thymus, crucial for the adaptive immune response, playing roles in cell-mediated immunity and the activation of other immune cells.

Opsonization

The process where pathogens are marked for destruction by immune cells through the binding of antibodies or complement proteins.