JG

Inverse Functions and Related Concepts - Comprehensive Notes

Inverse Functions: Core Idea

  • Inverse functions exist when a function is one-to-one (injective). If f is one-to-one, there is a function f^{-1} that "undoes" f.
  • Key relations:
    • If y = f(x), then x = f^{-1}(y).
    • Compositions yield identity: $$f^{-1}(f(x)) = x \