AMC 10/12 · Cheatsheet

Topic 1 · Algebra

Chapter 6 · Functions

📋 Reference · always available

Composition

f(g(x))\;\text{— inner machine first}

Inverse

Swap

x,y

then solve;

f(f^{-1}(x))=x

Domain

Exclude division by 0 and negatives under even roots.

Fixed point

f(x^*)=x^*

Iteration freezes there.

Cycle of period $k$

f_k(x_0)=x_0

, no smaller

j

. Value depends on

n \bmod k

Counting pre-images

f

m

-to-1 ⇒

f_n

typically

m^n

-to-1.