Section%202.7

Section%202.7 - o 6 F693 9%“ MA 180 ~ Precaiculus...

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Unformatted text preview: / o? 6 F693 9%“ MA 180 ~ Precaiculus Professor Terry Section 2.7: Operations on Functions E Sum Difference Product and Quotient of Functions <f+g)<x)= ‘ m + 106 (f-g)<x)= m - Cod (fg)(x)= C50 ° 1 (Jo) ' g 3 Ce) I 7 For f(x)=—x2 and g(x)=2x—I find: :7 9(3) 2. -(a) g. ‘ a)(f+g)(3) bur—gm) c) (fg)(3) d)(f/g)(3)- / .9033 amn z @thfld : 9Cx§+fiCbc\ : —)<2+c:lx~| , ‘ (9433(3) :2 ._C33'2—{c2(3-)*i :‘q—iohi 2~3wiafl @6933“) z “Kl-*C-M—O Z *XQHZx-H H 6—3,) (a) 2 “(339‘ 9—(33‘H z "Ci—(rm =-|S-il=-IL1' @ (agaXy) 2i C—xl) (’oxefl '2 ~2x5+x1 ; ($93003 2 were (are wem CL." ; (X "P :X—2 E: w ~05); 2 ___ci 2415 Q (3) 3 9X4 Lrj—MBE e 928}! I 5 For f(x)=x2 +x and g(x) =3:2 —3 find: § 8) (f +g)(x). (f —g)(x). (ngx). (f/gXx) b) the domain of f+g, f—g, fg c) the domain of f/g MA180 8902.7 Fall05 ewt A function f is a polynomial function if f(x) is a polynomial —that is if rm - C; n . f(x)= -an5L "i‘ ah_‘x ‘l' "i‘ QIX lttLt where the coefficients an [Cindi , m t 1 67v; ‘4‘ Ho are real numbers and the exponents are nonnegative integers _ i ‘ 3qu Q x a ’i x ~ 3 An algebraic function is a function that can be expressed in terms of finite sums, differences, products or quotients or roots of polynomial functions. Emotions that are not lgebraic are 4m“ C566“ 313‘ V1 . TWO examplesif h. ’ ' to, mm Beadat} functions are 612 EL CLK and AW functions. Corn osite Functions The domain of og is the set of all x in the domain of g such that g(x) is in the domain of f. “no: (image go?- is' wwaflx ml £00 15;; w' rim: dmtaficfj' For f(x)=3x2 and g(x):-x-1 find: 8) (f°g)(x) b) (g°f)(x) 0) (f°f)(x) d) (g°g)(x)- (9053(2) ? 836300) .2 QCX-Q 1 3Cx~©a 2338-9ch 38 g; (3 013300 r afloat) = 8&6?) 2 (“than 2 Big—{kg 60% = m sea 2 3w 2 m3 C011 @683650 2 MM): 300.) z 990“. For f(x)=3x-—l and g(x)=4x2 find: 3) (f°g)(x) b) (g°f)(x) O) f (g(-2)) d) g(f(3))- @@v3)(i¢3 rgfgai): ¥(le2):3(%2)*( 'ZE—Qxéfij grip—Ana 1520—2324 712(Lfl-i 21m /‘ 9mm): gflut—zflz @(wifiiicivi :(Ln @ (gowmu 3mg »: wax—o = stuffs" "z Li(%<7’~(e><+ i) 1’ 30x2~ZLiX ~H.{ MN"; __ MA‘iSOSecZJFalIDSe-MQ’ 2 fipgjfl‘z Ll(%)l 2 39(332»2w(a\+Liz—1§33 “‘“PW " R x 7/ o For f(x) ='—x2 +1 and g(x) :6 find: ' a) (fog)(x) and the domain of fog b) (gof)(x) and the domain of gof. @QOSyy-j 2 963cm)? 36(4) 2 -653?“ :3- —.x+[ K—bommum': X30 @ 093(1) 2 3(9—0082 gfi—XLHE z. W PM *XQ’H 2,0 QM 0>/X2—‘i “"XQ‘HV/O X2420 legit i742 "Imicva/s (“90,“(3 4‘1] [i :w) i 7/ixi de! + + " i > > ——i x 3 . l / X / For f(x)=x_2 and g(x)=; flnd‘ -———-—~ ‘ —~ { 5 X E i a) (fog)(x) and the domain of fog b) (go f )(x) an/d the domain of go;ifi_g__#@m_ N) Z / ‘2 i z 3 X :- 3 72‘ ' @ 6 03X“, g: (@163 34:1 35 82—331 03% ' Xfié Q ‘ 36% O Q ‘_ ‘ (5203300 3— QX4O 8 " X4 0 X4 3/31 ‘ o C 2 v 2 2 ———~3——— 9 >53“ 2 300 33H 3&4; <9 (3 Q) n 3 9 mi 3 (x3 if 6%) m X - T Several values of two functions are listed in the following tables: + T _ ‘ I_ 0 a? I. E- r Find: a) (ToS)(1) b) (SOT)(1) c)(ToT)(1) d) (SoS)(1). 0 @fingct) 2 'T (60)) :2 ‘TCO\ “2 @ @(gmm 2' 36mm} 2 3(3) 2 [(3] @ ($60) 2 Tf'im) 2 T5) 2 E31 MA1808eQ.TFaII05eM(gD%) : 5(5(O):$ (o) t m Dimensions of a balloon A spherical balloon is being, inflated at a rate of 2;: fr3 /min. 2 Express its radius r as a function of time t (in minutes), assuming that r = 0 and t: 0. given Fair? 0? 2 fig.“ gig/nun“ 1 Find a composite form for y, if y =—2——3. (x +3x—5) MA'180 Sec2.7 Fall05 ewt ...
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Section%202.7 - o 6 F693 9%“ MA 180 ~ Precaiculus...

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