section27

# section27 - A one-to-one function is a function where each...

This preview shows pages 1–3. Sign up to view the full content.

MAT 111 - College Algebra Section 2.7: Inverse Functions Consider the function f ( x ) = { (1 , a ) , (2 , b ) , ( - 3 , e ) } D f : R f : Notice that for every x in the domain of f there exists a unique value y in the range of f . Moreover, associated with every y in the R f there is a unique x in D f . A function and its inverse undo the eﬀect of each other. That is, ( f f - 1 )( x ) = x and ( f - 1 f )( x ) = x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
How to determine if two functions are inverses of each other: Examples: Determine if the given pairs of functions are inverses of each other. 1. f ( x ) = 2 x and g ( x ) = x 2 2. h ( x ) = 3 x + 1 and g ( x ) = x - 1 5 Q: Do all functions have inverses? NO , only one-to-one functions have inverses.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A one-to-one function is a function where each value of the dependent variable is assigned to exactly one value of the independent variable. Determining one-to-one functions graphically: use horizontal line test. How to ﬁnd inverse functions: 1. Numerically: 2. Graphically: 3. Algebraically: (a) Write y = f ( x ) (b) Interchange x and y . (c) Solve for y in terms of x (d) Write y as f-1 ( x ) Examples: Find the inverse function for each of the following functions: 1. g ( x ) = 3-x 4 2. h ( x ) =-5 x + 1 x-1...
View Full Document

## This note was uploaded on 01/17/2012 for the course MATH 111 taught by Professor Carolineboulis during the Fall '10 term at Lee.

### Page1 / 3

section27 - A one-to-one function is a function where each...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online