Mathematics: Applications and Interpretation · Topic 2: Functions

AHL2.7 — Composite and inverse functions

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AIAHL2.7.1

   Composite functions

   $(f\circ g)(x)=f(g(x))$: apply $g$ first, then $f$; order matters and domains must be compatible.

2. AIAHL2.7.2

   Inverse functions and domain restriction

   $f^{-1}$ reverses $f$ with $(f\circ f^{-1})(x)=(f^{-1}\circ f)(x)=x$; restrict the domain so $f$ is one-to-one.