Answer:
The inverse of a non-function mapping is not necessarily a function.
For example, the inverse of the non-function mapping 
is the same as itself (and thus isn't a function, either.)
Step-by-step explanation:
A mapping is a set of pairs of the form 
. The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.
A mapping is a function if and only if for each possible input value 
, at most one of the distinct pairs includes 
as the value of first entry.
For example, the mapping 
is a function. However, the mapping 
isn't a function since more than one of the distinct pairs in this mapping include 
as the value of the first entry.
The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping 
is the mapping 
.
Consider mapping . This mapping isn't a function since the input value 
is the first entry of more than one of the pairs.
Invert as follows:
becomes .
becomes 
.- becomes .
becomes .
In other words, the inverse of the mapping would be 
, which is the same as the original mapping. (Mappings are sets. There is no order between entries within a mapping.)
Thus, is an example of a non-function mapping that is still not a function.
More generally, the inverse of non-trivial ellipses (a class of continuous non-function 
mappings, including circles) are also non-function mappings.
