Final answer:
The inverse relation of the given function does represent a function because after swapping the x and y values, each input of the inverse relation maps to exactly one output, fulfilling the requirement for a set of points to be a function.
Step-by-step explanation:
The student is asking whether the inverse relation of a given function represents a function itself.
The function provided is f= {(-1, -1), (3,3), (9,0), (0,9)}.
To determine if the inverse represents a function, we swap the x and y values in each ordered pair to get the inverse relation which will be f^{-1}= {(-1, -1), (3,3), (0,9), (9,0)}.
Next, we check if each input (now the first value in each pair) maps to exactly one output.
Since none of the inputs are repeated in the inverse relation, the inverse does indeed represent a function.
This exercise involves understanding the concept of functions and their inverses, which relies on the definition that for each input, there must be exactly one output in a function.
Recalling that the inverse of a function 'undoes' the function, just like natural log and exponential functions are inverses of each other, we can confirm that in this case, the inverse of the given set of points does indeed form a function because it adheres to the definition.