Inverse Hyperbolic Functions

This lecture focuses on the study of inverse functions to hyperbolic functions, emphasizing the parallels with trigonometric functions. By explicitly reversing hyperbolic relations, concrete expressions for inverse hyperbolic functions are derived. The lecture covers the properties of inverse hyperbolic functions, such as Arsh(x) = ln(x + √(x² + 1)), and Arch(x) = ln(x + √(x² - 1)). The lecture also discusses the restrictions on the domains of these functions to ensure bijections. The derivatives of Arsh(x) and Arch(x) are derived and verified. The lecture concludes by summarizing that sinh(x) is a bijection between R and R, while cosh(x) is a bijection between R+ and [1, ∞[.