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

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

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