Is it possible to have an explicit formula that is not a function?

Yes, it is possible to have an explicit formula that is not a function. A classic example is the equation (y^2 = x), which defines (y) in terms of (x) but does not satisfy the definition of a function because for some values of (x), such as (0), there are two corresponding values of (y) (specifically, (y = 0) and (y = -0)). In general, an explicit formula can represent a relation that assigns multiple outputs to a single input, thereby violating the functional requirement of one output for each input.