4. A function consists of the pairs (2,3), (x, y) and (5,6). If the inverse is also a function what values can y NOT be? Explain.

Answer:
In a nutshell, [tex]y[/tex] cannot be 3 or 6 in the inverse function for all [tex]x[/tex] distinct from 2 and 5.
Step-by-step explanation:
From Functional Theory we remember that a function is a relation in which all elements of its domain has an unique and different element from range. If [tex]y[/tex] is the image of the inverse, which is a function, then [tex]y \neq 3, 6[/tex]. Otherwise, the inverse could not be a function when [tex]x \in \mathbb{R}-\{2,5\}[/tex].
In a nutshell, [tex]y[/tex] cannot be 3 or 6 in the inverse function for all [tex]x[/tex] distinct from 2 and 5.