Are these functions invertible?

[IntegrateMe]

Just a yes or no. It would help to know why, also.

1. f(d) is the number of orange woolen hats sold at a department store on the dth day after September 1, 2003.

2. f(w) is the cost of mailing a letter weighing w grams.

3. f(t) is the total accumulated rainfall in inches t minutes into a sudden rainstorm in July, 2005.

I thought the answers were no, yes, no, respectively, because the first and third instances deal with particular instances, but, apparently, I'm wrong. Any help?

 

[Mark44]

Just a yes or no. It would help to know why, also.

1. f(d) is the number of orange woolen hats sold at a department store on the dth day after September 1, 2003.

2. f(w) is the cost of mailing a letter weighing w grams.

3. f(t) is the total accumulated rainfall in inches t minutes into a sudden rainstorm in July, 2005.

I thought the answers were no, yes, no, respectively, because the first and third instances deal with particular instances, but, apparently, I'm wrong. Any help?

I would say no, no, yes for these. If a function is invertible, you can deduce the input value from the function's output value. For the first problem, if 2 woolen hats are sold on the 3rd day and 2 more on the 6th day after 9/1/2003, then 3 is paired with 2 and 6 is paired with 2, making this function not one-to-one, and hence noninvertible.

For the 2nd problem, the way it works in real life is that letters with slightly different weights take the same amount of postage, so here again we have a function that is not one-to-one, which means that it is noninvertible.

For the 3rd problem, assuming that rainfall accumulates, here we have an increasing function for which different times imply different amounts of rainfall. That makes this function one-to-one, and so it is invertible.