Class Notes (837,186)
Canada (510,155)
Mathematics (1,919)
MATH 137 (135)
Lecture

1-1 functions, Inverse & Trig Functions, Intro to Limits

5 Pages
118 Views
Unlock Document

Department
Mathematics
Course
MATH 137
Professor
Jennifer Nissen
Semester
Fall

Description
Lecture 5 11PreviouslySeptember2111827 AMExample 45Prove that if 0 2 then cossin 1DefinitionA function f is called onetoone 11 if it never takes the same value twiceThat is ifthen fx1 fx2Or if fx1fx2 then Example 51 Prove that fxwith domain Df1is 11ProofSuppose f ffor some x xDf12Then2 2x xx x xx 01122 12 22x x xxxx 01 21212xx xxxx01 21221What is BCxx1 xx01212BCsin Arclength of BATherefore x xor xx 11212Arc BAIf x x we are done12If xx 1 then since xx 1 Df1 x x 1121212Note BCBAarc BAsinBAIn both cases x x so f is onetoone12Notethus sinso1If we consider gxwith domain Dg0then gx is not 11 Intuitively arc BABEEAeg g2g25DA tanHorizontal Line TextSo arc BAtansotanA function f is 11 if and only if no horizontal line intersects its graph more than So cos sinonce cos NoteIncreasing and decreasing functions are 11Therefore cos for 0 Inverse Functions 1If f is 11 with domain DfA and range RfB then its inverse function fexists 1with domain B and range A and is defined by fyx if and only if fxy1To find f we solve fxy for x in terms of yExample 522Is the function gxx2 11 No2But fxx2 with domain Df0is 111Find f2yx22y2xx 1Since RfDf0then it must be1 ie fy 1 Df2 Rf MATH 137 Page 1
More Less

Related notes for MATH 137

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit