Why does InverseFunction[0 &]@0 return 33/10?

In Mathematica 8.0.1.0 on 32-bit Linux, the expression

InverseFunction[0 &]@0

returns 33/10. (The same occurs for other integer and rational values; I'm using 0 as an example.)

According to the documentation for InverseFunction:

As discussed in Functions That Do Not Have Unique Valu开发者_如何转开发es, many mathematical functions do not have unique inverses. In such cases, InverseFunction[f] can represent only one of the possible inverses for f.

As a constant function 0& will return 0 regardless of its input, it has infinitely many inverse functions (each of which is defined only at 0). So as defined, this answer is within the specification.

The mystery is, why does it give 33/10 rather than any other value?

That number appears in a number of instances. Take for instance:

FindInstance[x == x, x, Reals]

{{x->33/10}}

I've seen discussions of this number come up before. It's basically just some result of how Mathematica is implemented. You'll get this sometimes when you ask Mathematica to do something that boils down to "Pick a Random Real number". It doesn't have any real special meaning.