Let F assign each student in the math department his/her biological father. Explain why F is a function. (a.) Describe conditions on the situation above that would have to be true in order for F to have an inverse. (b.) In a case from part (a.) in which F does not have an inverse, can you modify the domain so that it does? Solution F is a function since it is mapping each student to his/her biological father. Which is the basic requirement of any mapping for it to be a function. In simple words all the domain elements should be mapped to some elemens in the range. (a) In order for the existance of F Inverse F must be one one and onto. i.e. no two students should have the same biological father and every biological father must have exactly one child. (c) For modifying F to be Inverse the domain should contain only those students among whom no two students are the siblings of each other so that it satisfirs the one one condition, making F Invertible. .

1. Let F assign each student in the math department his/her biological father. Explain why F is a
function.
(a.) Describe conditions on the situation above that would have to be true in order for F to have
an inverse.
(b.) In a case from part (a.) in which F does not have an inverse, can you modify the domain so
that it does?
Solution
F is a function since it is mapping each student to his/her biological father. Which is the basic
requirement of any mapping for it to be a function.
In simple words all the domain elements should be mapped to some elemens in the range.
(a) In order for the existance of F Inverse F must be one one and onto. i.e. no two students should
have the same biological father and every biological father must have exactly one child.
(c) For modifying F to be Inverse the domain should contain only those students among whom
no two students are the siblings of each other so that it satisfirs the one one condition, making F
Invertible.