Section 4 1 inverses
This presentation is the property of its rightful owner.
Sponsored Links
1 / 7

Section 4.1: Inverses PowerPoint PPT Presentation


  • 45 Views
  • Uploaded on
  • Presentation posted in: General

If the functions f and g satisfy two conditions:. Section 4.1: Inverses. g(f(x)) = x for every x in the domain of f . f(g(x)) = x for every x in the domain of g. then f and g are inverse functions . f is an inverse of g and g is an inverse of f. Determine whether f and g are inverses:.

Download Presentation

Section 4.1: Inverses

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Section 4 1 inverses

If the functions f and g satisfy two conditions:

Section 4.1: Inverses

g(f(x)) = x for every x in the domain of f

f(g(x)) = x for every x in the domain of g

then f and g are inverse functions. f is an inverse of g and g is an inverse of f


Section 4 1 inverses1

Determine whether f and g are inverses:

Section 4.1: Inverses

f and g are inverses


Section 4 1 inverses2

Method for determining the inverse of a function:

Section 4.1: Inverses

Solve for x:


Section 4 1 inverses3

A function f has an inverse if and only if its graph is cut at most once by any horizontal line:

Section 4.1: Inverses

A function which passes the vertical and horizontal line tests has an inverse and is one-to-one.


Section 4 1 inverses4

Graphically:

Section 4.1: Inverses

If f has an inverse, the graphs of the functions are reflections of one another about the line y = x.


Section 4 1 inverses5

If the graph of f is always increasing or decreasing, then the function f has an inverse.

Section 4.1: Inverses

How can we show a function is always increasing or decreasing?


Section 4 1 inverses6

The domain of the original is the range of the inverse. The range of the original is the domain of the inverse.

Section 4.1: Inverses


  • Login