section7_1 - Section 7.1 Inverse functions A function f is...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 7.1 Inverse functions
Background image of page 1

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

View Full DocumentRight Arrow Icon
A function f is invertible if It can be reversed. You can find an inverse function f -1 which undoes whatever f does.
Background image of page 2
Which functions are invertible?
Background image of page 3

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

View Full DocumentRight Arrow Icon
Which functions are invertible? f: A B is invertible iff f is one-to-one on A distinct inputs give different outputs: If x 1 x 2 , then f(x 1 ) f(x 2 )
Background image of page 4
From the formula of f: check f(x 1 )=f(x 2 ) x 1 =x 2 From the derivative of f: f’(x) does not change sign From the graph of f: horizontal line test for f ( x ) = x , x 1 = x 2 ! x 1 = x 2 Mvc,b.cvb f’(x)>0 for all x f’(x)<0 for all x not one-to-one
Background image of page 5

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

View Full DocumentRight Arrow Icon
Question The function y=(x 3 +7x) 133 is invertible. True False
Background image of page 6
Question The function f(x)=(x 3 +7x) 133 is invertible. True False f’(x)=133 (x 3 +7x) 132 (3x 2 +7) is zero at a single point, and is otherwise positive, so f is increasing.
Background image of page 7

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

View Full DocumentRight Arrow Icon
Question No even function is invertible (in its full domain). True False
Background image of page 8
Question No even function is invertible (in its full domain). True
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/07/2010 for the course MATH MATH 2B taught by Professor Famiglietti,c during the Fall '09 term at UC Irvine.

Page1 / 25

section7_1 - Section 7.1 Inverse functions A function f is...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online