A strictly increasing function is, well, exactly what it sounds like. If x > y, f(x) > f(y). Try to visualize this. It never changes direction, never doubles back on itself. So there’s always an inverse, for every output, there’s always a unique input.
Strictly increasing guarantees the function is one-to-one. However, it also needs to be onto to guarantee an inverse exists. Of course, you can restrict the codomain to the image of the function, but anyhow...
And yeah, given that the functions in question are intended to be “translators” from one way of numerically encoding one’s preferences to another, restricting the codomain to the range would be implicit in that, I guess.
But yeah, strictly speaking, you’re definitely right.
Minor quibble:
Strictly increasing guarantees the function is one-to-one. However, it also needs to be onto to guarantee an inverse exists. Of course, you can restrict the codomain to the image of the function, but anyhow...
Fair enough.
And yeah, given that the functions in question are intended to be “translators” from one way of numerically encoding one’s preferences to another, restricting the codomain to the range would be implicit in that, I guess.
But yeah, strictly speaking, you’re definitely right.