I was not able to confirm this bug fact, hard to search a math theorem without a name. If anyone knows what this theorem is called and if it is true id be glad to know
Cool, didn't think of that one. But it would still work, since you could consider that a constant in front of the f(x) not raised to the nth power (easier to imagine if we have a constant function, then its just (b-a)). The nth root will then normalise it to 1 for any real factor.