1013 Lecture 12 PDF

22.3 Lecture  blank PopQuI the fill in t i It an Tangle B Eft t...

22.3 Lecture  blank PopQuI the fill in t i It an Tangle B Eft t Tatsa inverse f and f has domain B ano range A In symbols A.fi xc 7fcxl y y for y EA any B fax f ly x y f fax C ly y values x for all real y f fax ly x y for y E B any Recall last class we said we can build inverse for functions that are not l l by a this creates restrictingthedemand function that is l l and therefore new has an inverse with domain O W is 1 1 fax ex n x2 and range 0,0 f domain ox is 1 of 0,01 and Sx is range O X functions where another important class of functions we have to do this are trig since ex y Image t.is A fails the HLT often Aly so it is ifff.fi gmittt definitely not 1 1 i t we restrict the To force it to be 7 domain to Tia 2  Tom range g arcsincx I i 1 Him yc xforan 7sinlyl 0 farcsincxl m.tt for C T2 T2 sin sinixt arc frgf x for XG 1 1 sin aresinch ÉÉ domain IR cos x with ex y A fails HCT Aly offer f  restriction for the domain is Co I The usual range is 1,1 48 cosm i it Tti 4 arcrossy has domain C 1,13 CC I range we have From this for fafn any y.to re arccos for O T loscx any EYE for e 1,1 cos larcosan any  tank with domain IR E y fails HLT 1 sly often I l i f I I 1 domain tan x restrict the of we usually x x to 712 712 range on t tann afferent range 14th 1 I ay f I in IV  arctance Eharctances has rates ftp.narctancxs the noria F fxtta 71 gg X for all E 1 E JE arctan tances x x for alexe tan arctances Elif determine what use desmos to exc use for secex Esc x domain would latex add these defins before note to Allysa posting Towbacktoimlicitdifferentiation diff is to be A use of implicit key derivatives inverses able to take of  Recall f x y fly forgetdomf f can use this to create a formula for we an inverse the derivative of we know the derivative of fan suppose we want to ffidfgwnenyf de f ex hard but I do know the derivative of fly let's consider flyl fly 1 fly dy rule I dx chair is a remember y function x Fca x  find if In x ex y Incx c e x for all note Soh y yer approach long Totocompute let's use et es 1 91 tey dy in shortaffordia incx is the inverse of e se use note Einen te for some bro let y logbly b 1 Find dg  note logs x is the inverse of sof our formula gives bx So logbly tantrum x̅ find ex let g arcsiney 1 inverse sin note arisincy is the of Sol the formula so we can apply arcsina rcsinc this by using a triangle we can simplify arcsincx c sincy y by Pythagorean than we know 7 12  1 1 x2 Fx recall yearssincy we need to know coscaresinen so cosca EI 1 1 arssinm f arccosyl and exe compute arctance add these solins Cote for Allysa