Final answer:
The inverse of the relation y ≤ -x² is not standard as inverses are typically defined for functions, and inverses of inequalities do not have a single definition. Inverse relationships, in general, involve switching x and y, but with inequalities, we often discuss solutions or graph the regions they represent instead.
Step-by-step explanation:
The inverse of a relation essentially reverses the roles of the variables. For the given relation y ≤ -x², the inverse would reverse the x and y variables. However, because the original relation describes a set of ordered pairs where y is less than or equal to the square of the negative of x, inverting this is a bit complex. It's not a function, so referring to it as an inverse function is technically incorrect and the inequality complicates matters further. Inverse relationships typically involve switching the dependent and independent variables. However, with an inequality, you don't usually discuss an inverse in the same way as you would with an equation, because inequalities represent regions rather than specific relationships between variables.
An inverse relationship in physics, such as Coulomb's law or the relation y = k/x, indicates that one variable decreases as the other increases, which is different from the given relation of y ≤ -x². Nonetheless, if you are looking for an inverse proportionality, where for each x there is precisely one y, it's more complex because the given relation is not a function due to the ≤ sign.