1 / 9

Understanding Inverse Functions in Calculus

Learn about one-to-one functions, inverse functions, rules, notation, finding inverses, and special numbers like e in calculus.

bunderwood
Download Presentation

Understanding Inverse Functions in Calculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math 1304 Calculus I 1.6 Inverse Functions

  2. 1.6 Inverse functions • Definition: A function f is said to be one-to-one if f(x) = f(y) implies x = y. • It never takes on the same value twice • Horizontal Line Test: A function is one-to-one if and only if no horizontal line intersects its graph more than once.

  3. Inverse Functions • Definition: Let f and g be functions. They are said to be inverse if y = f(x) ↔ g(y) = x • Theorem: If f is a one-to-one function then it has an unique inverse. • Notation: the inverse of f is denoted by f-1

  4. Rules for inverses • f-1(f(x)) = x, for all x in the domain of f • f(f-1 (x)) = x, for all x in the domain of f-1

  5. Finding an inverse • Write y = f(x) and solve for x in terms of y.

  6. Logarithms are inverse to exponentials • loga(y) = x iff y = ax

  7. Laws for logarithms • See page 64

  8. Natural Logarithms • Natural = base e • ln(x) = loge(x)

  9. The number e • e = 2.718281828… is a special number that is used as a base for exponential functions in calculus

More Related