[Verse 1]
From domain A to codomain B
A function maps with precision key
Not every arrow needs a formula's face
Just one output for each input's place
Your birthday mapped to calendar squares
No equation needed, just who goes where
[Chorus]
One input, one output, that's the sacred rule
Domain to codomain, mathematical tool
Image shows where outputs actually land
Preimage traces back through function's hand
Mapping is the magic, not the written form
One-to-one assignment keeps the function warm
[Verse 2]
Domain holds the inputs waiting in line
Codomain's the space where answers align
But image tells the truth of where we really go
Subset of codomain, the actual show
F inverse of S pulls backwards through time
Finding every input that crossed that line
[Chorus]
One input, one output, that's the sacred rule
Domain to codomain, mathematical tool
Image shows where outputs actually land
Preimage traces back through function's hand
Mapping is the magic, not the written form
One-to-one assignment keeps the function warm
[Bridge]
Real numbers squared or names to dates
Functions live beyond formula gates
Relation yes, but special kind
Uniqueness keeps the mapping refined
[Chorus]
One input, one output, that's the sacred rule
Domain to codomain, mathematical tool
Image shows where outputs actually land
Preimage traces back through function's hand
Mapping is the magic, not the written form
One-to-one assignment keeps the function warm
[Outro]
Every element must have its mate
Exactly one, that seals function's fate