[Verse 1]
When functions dance in sequence neat
From A to B, then B to C
First f takes you to the street
Then g completes the journey free
We write it backwards, strange but true
G circle f means f then g
The path flows through what functions do
A straight shot to your destiny
[Chorus]
Composition chains them tight
Read it backwards, left to right
First apply f, then apply g
G circle f is what you see
Properties preserve their might
Injective stays injective bright
Surjective keeps its surjective flight
Bijective holds bijective sight
[Verse 2]
When arrows point from set to set
The middle link must always match
Domain B can't be upset
It bridges every function batch
Associative like multiplication
Parentheses can shift around
But order matters, no equation
Commutative can't be found
[Chorus]
Composition chains them tight
Read it backwards, left to right
First apply f, then apply g
G circle f is what you see
Properties preserve their might
Injective stays injective bright
Surjective keeps its surjective flight
Bijective holds bijective sight
[Bridge]
G of f of a, that's the rule
Apply the functions like a tool
One-to-one stays one-to-one
Onto stays when composition's done
H circle, G circle F
Grouping changes, result's the same
But flip them round, you'll need your breath
G circle F and F circle G aren't the same game
[Outro]
Function composition's art
Backward notation, forward heart
Chain reactions, pure and clean
Mathematical machine