Answer:
a) There cannot be sibling in the class.
b) This larger function would have an inverse only if there are no siblings studying in the same school.
Explanation:
The inverse of a function f is a function g that "reverses" f. In other words, if the function f is applied to an x and it gives a result of y, then applying the function g to y gives the result of x. f(g(x)) = x.
For a function f to have an inverse, the function f has to give only one value y, when applied to an x.
a. In order for f to have an inverse, what condition must be true about students in the class?
So now, we have that f assigns each student in the class her biological mother.
Therefore, the set of X formed by the students in the class
And Y refers to their biological mother.
If we want f to have an inverse, then each mother should be assigned to only one student.
This means that the condition that must be true is that there cannot be brothers/sisters in the same class (for example, twins).
b. If we enlarged the domain to include all students in the school, would this larger domain function have an inverse.
Applying the same thinking, for f to have an inverse, every mom should be assigned to only one student.
Therefore, for this larger domain, there shouldn't be brothers/sisters studying in the same school.