1 / 8

Ch 9 – Properties and Attributes of Functions

This section explores the properties and attributes of functions, focusing on their inverses. The inverse of a function "undoes" the operation of the original function and is represented as f⁻¹(x). Its graph is a reflection across the line y = x. The horizontal line test is utilized to determine if the inverse is a function. The process of finding an inverse involves switching x and y and solving for y. Additionally, we discuss the characteristics of one-to-one functions and how to verify inverses through composition.

maida
Télécharger la présentation

Ch 9 – Properties and Attributes of Functions

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. Ch 9 – Properties and Attributes of Functions 9.5 – Functions and their Inverses

  2. What is the inverse of a function? • The inverse of a function f(x) “undoes” f(x) • Its graph is a reflection of f(x) across the line y = x • Sometimes, the inverse ends up NOT being a function. • If the inverse is a function, then it is denoted as f-1(x)

  3. Horizontal-Line TestIf any horizontal line passes through more than one point on the graph of a relation, the inverse relation is NOT a function. The inverse relation is a function The inverse relation is not a function

  4. Use the horizontal-line test to determine whether the inverse of each relation is a function.

  5. Finding Inverses of functions • To find the inverse of a function, switch the x and y, then solve for y. • Example: Find the inverse of f(x) = x2

  6. Find the inverse f-1(x) of Determine whether it is a function, and state its domain and range.

  7. In a one-to-one function, each y-value is paired with EXACTLY one x-value. You can use composition of functions to verify that two functions are inverses. If f(g(x)) = g(f(x)) = x then f(x) and g(x) are inverse functions. When both a relation and its inverse are functions, the relation is called a one-to-one function.

  8. Determine by composition whether each pair of functions are inverses.

More Related