Question

(1.) decide if function f is invertible.
a) f(n) is the number of students in your calculus class whose birthday is on the nth day of the year.
b) f(x) is the volume in litters of x kilograms of water at 4 degrees celsius.

Answer 1

a doesnt not have an inverse

Answer 2

so therefore its irrevertible?

Answer 3

Okay, so if f(n) is the number of students whose birthday is on the nth day of the year, then n is a day of the year, and f is how many students have a birthday on that day. For demonstration, lets assume that on days n = 1, 2, 3, the students in your class have 1 birthday, 2 birthdays, and 2 birthdays, respectively.

so n=1 maps to 1, n=2 maps to 2, and n=3 maps to 2. This is a problem because both n=2 and 3 map to 2. Therefore it is not one-to-one, and the inverse of f(n) is not possible.

Answer 4

B does not have this problem. Since 2 kilograms of water will take up more volume than 1 kilogram of water, and 3 kilograms of water will take up more volume than 1 or 2 kilograms, there is no* pair of kilograms of water that share volume. To add or subtract volume, you must add or subtract water, which will change the kilograms.

Hence, the function described in B is one-to-one and can be inverted.


*If you rounded your measurements enough its possible you could noticeably change one measurement without noticeably changing the other, but that's a different question

Answer 5

alright so just clarifying, a is NOT invertible and b is?

Answer 6

Correct, A: No, B:Yes

Answer 7

thank you!

Answer 8

No problem