Quick Recap — Counting, Functional Equations & Range (Hard)

Chain several ideas: surjection counts by inclusion–exclusion, functional equations (f(x+y)=f(x)+f(y)f(x+y)=f(x)+f(y) etc.), and range of rational/trigonometric functions via the discriminant or R=a2+b2R=\sqrt{a^2+b^2} bound. Many are numerical-value (Section B), and some fuse with trigonometry, quadratics and sequences.