1.8(one) - 1.8 Inverse FunCtions Verifig inverse...

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Unformatted text preview: 1.8 Inverse FunCtions Verifig inverse functions. Inverse Functions are 1:1 Reminder: The definition of function is, for every X there is only one y .. - m: X .1. ‘161‘17’ih warm?“ ‘ , _. , *7 " We a X ‘53 ‘ __‘{.¥igifliiiiflfi I; “a; 3i {SEER-1%? a) “a m i i {nefiufifi mom: *3” 1;“ 52‘}:- ' ‘ . .‘ r ",1- " I" ‘ a 11%?" 9”" t“. “1111313 ' . x “fin , 1g . Find f(g(x)) and g(f(x)) using the following functions to ShOW that they are inverse functions. X—2 X : .— g( ) 3 : Ham): ALE-"39+ & : x—a+9\ Find the inverse of a function. mailing; the Inverse a Emitting: . The equation fer-11m inverse of a function f ean be feunri as feiimvs: 3!; Replace fix} wiiliy in the equation fer fix}. '2‘. interchange 3c and 3;. 1i. Soie‘e far 3!. If this aquarium tines. not; define. 3;. as it iiuaetien of at, the. function 3“ times not have an; inverse fimctiinu and: .tiiis-pmcfiéure ends. if this retina» lion dues define 3: aa- a :iigmetiien ai?.it.yt]1e;£anuiien.f hams: imam: 'Ifflflfiiiim. Iii f has an inverse mama. replaces Waste? 3 by Fig}. We can verify our result? hyahmtting.:thagtgi’fifmifiei) ‘g- xafifi j‘fléffixfi ? .12 The function f is a set of ordered pairs, (x,y), then the changes produced by .f can be “undone” by reversing components of all the ordered pairs. The resulting relation (y,x), may or may not be a function. Inverse functions have a special “undoing” relationship. Find the inverse of f(X)=7X-l : :i-X ’“l SH} X—I—IT—qr'j “JD/ 231:3! "3mg: (j m: 293.1 swig '“l (1206 5+2 l f(x)=2:+_13’ find f4” ‘3: \C/ @433— X—H CW K : 7:14;; Q 5 ldfl 31%;)- @rH)K-:2er3 ' ‘dxq—K : Z—jreB fo I X113 :th’jx 2% .- X+ : “ 3 30' K) 4 x y 2:12;.— - 0 " 1P3 + er '3 at y H—firfli mi— 3 r? ax 3 via: a » +3Lx+0 ‘ H ) [ WI) T Use the horizontal line test to determine if a function has an inverse function. Horizontal-lime Test If every horizontal line intersects the graph of a function f in at most one point then f is one~to—one. ...
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This note was uploaded on 01/16/2012 for the course MATH 126 taught by Professor Blisinhestiyas during the Fall '11 term at Truckee Meadows Community College.

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1.8(one) - 1.8 Inverse FunCtions Verifig inverse...

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