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Fungsi Invers dan Fungsi Komposisi 1. Fungsi f(x) = 2x – 3, maka f -1 (x) = … Jawab : f(x) = y y = 2x – 3 y + 3 = 2x = x Jadi, f -1 (x) = 2. Fungsi f(x) = , maka f -1 (x) = … Jawab : f(x) = y y = 2xy – 5y = 4x + 3 2xy – 4x = 3 + 5y x(2y – 4) = 3 + 5y x = Jadi, f -1 (x) = 3. Fungsi f(x) = x 2 + 1, maka f -1 (x) = … Jawab : 1
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### Transcript of TUGAS KALKULUS

61 ) (x g= 4 626) ( 2+x g= 4 31) (31+ x g= ) (31313x g Jadi, f(x) = x3131323. Diketahui (g o f)(x) = 1 12 42+ x x dan f(x) = 2x 3, tentukan g(x) = Jawab :(g o f)(x) = 1 12 42+ x xg(f(x)) = 1 12 42+ x x f(x) = 2x 3f(x) + 3 = 2xxx f+23 ) (g(f(x)) = 4 123 ) (1223 ) (2+

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+

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+ x f x f= 1236) (21249 ) ( 6 ) (42+

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+ +x fx f x f= f(x)2 + 6f(x) + 9 6f(x) 18 + 110= f(x)2 8Jadi, g(x) = x2 824. Diketahui (f o g)(x) = x x +2dan g(x) = 2x + 1, maka tentukan f(x) = Jawab :(f o g)(x) = x x +2f(g(x)) = x x +2 g(x) = 2x + 1g(x) 1 = 2xxx g21 ) (f(g(x)) =

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+

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21 ) (21 ) (2x g x g= ,_

+

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+ 21 ) (41 ) ( 2 ) (2x g x g x g= ,_

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+ 42 ) ( 241 ) ( 2 ) (2x g x g x g= 41 ) (2 x gJadi, f(x) = 41414122x ataux25. Diketahui (f o g)(x) = 24 x dan g(x) = 12+ x , maka tentukan f(x) = Jawab :(f o g)(x) = 24 xf(g(x)) = 24 x g(x) = 12+ xg(x) 1 = 2xx = 1 ) ( x g11f(g(x)) = ( ) 2 1 ) (4 x g= 2 1 ) ( 2 ) (2 + x g x gJadi, f(x) = 1 22 x x 26. Jika f(x) = 2x 4 dan g(x) = 3x + 1, maka tentukan invers dari (g o f) -1 (x) = Jawab :Caranya, dikomposisikan dahulu kemudian di inverskan.(g o f)(x) = g(f(x))= g(2x 4)= 3(2x 4) + 1= 6x 12 + 1= 6x 11(g o f)(x) = yy = 6x 11y + 11 = 6x611 + y= xJadi, (g o f) -1 (x) = 611 + x27. Jika f(x) = 2x 4 dan g(x) = 3x + 1, maka tentukan invers dari (f o g) -1 (x) = Jawab :Caranya, dikomposisikan dahulu kemudian di inverskan.(f o g)(x) = f(g(x))= f(3x + 1)= 2(3x + 1) 4= 6x + 2 4= 6x 212(f o g)(x) = yy = 6x 2y + 2 = 6x62 + y= xJadi, (f o g) -1 (x) = 62 + x28. Jika f(x) = 3x 4 dan g(x) = 3x + 2, maka tentukan invers dari (f -1 o g -1) (x) = Jawab :Caranya, di inverskan masing-masing fungsi kemudian dikomposisiskan. f(x) = 3x 4f(x) = yy = 3x 4y + 4 = 3x34 + y= xMaka f -1(x) = 34 + x g(x) = 3x + 2g(x) = yy = 3x + 2y 2 = 3x32 y= xMaka g -1(x) = 32 xMaka, (f -1 o g -1) (x) = f -1(g -1(x))= f ,_

32 x13= 3432+ x= 331232+ x= 3310 + x= 910 + xJadi, (f -1 o g -1) (x) = 910 + x29. Jika f(x) = 3x 4 dan g(x) = 3x + 2, maka tentukan invers dari (g -1 o f -1) (x) = Jawab :Caranya, di inverskan masing-masing fungsi kemudian dikomposisiskan. f(x) = 3x 4f(x) = yy = 3x 4y + 4 = 3x34 + y= xMaka f -1(x) = 34 + x g(x) = 3x + 2g(x) = yy = 3x + 2y 2 = 3x32 y= xMaka g -1(x) = 32 xJadi (g -1 o f -1) (x) = g -1(f -1(x))14= g ,_

+34 x= 3234+ x= 33634+ x= 332 x= 92 xJadi, (g -1 o f -1) (x) = 92 xIntegral30. dx x adalah Jawab : x dx = 21x dx= 1212111 ++ x + c= 23231x + c= 2332x + c= 21.321x x + c= x x .321 + cJadi, x dx = x x .321 + c1531. dx x4 3adalah Jawab :dx x4 3= dx x43= c x +++1434311= c x +++444344431= c x +47471= c x +4774= c x x +4 374Jadi, dx x4 3 = c x x +4 37432. dxxx251adalah Jawab : dx x dx x dxxdxxxdxxx2 32 25251 1 = c x x ++ ++ + 1 2 1 31 211 31 = c x x +

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1 41141 = c x x + + 1 441= cxx + +1414Jadi, dxxx251 = cxx + +14141633. 21x dx adalah Jawab : 21x dx = 2xdx= 1 21 21 + + x + c= 111 x + c= 1 x + c atau cx + 1Jadi, 21x dx = 1 x + c atau cx + 134. + dx x x ) 2 (3 adalah Jawab : + dx x x ) 2 (3= + xdx dx x32= c x x +++++ + 1 1 1 31 111 32= c x x + +2 42142Jadi, + dx x x ) 2 (3 = c x x + +2 4214235. + dx x x x ) 2 4 (2 3 5 adalah Jawab : + dx x x x ) 2 4 (2 3 5= + dx x dx x dx x2 3 52 4= 1 2 1 3 1 51 221 341 51 + + +++++ x x x + c= c x x x + + 3 4 632446117= c x x x + + 4 4 63261Jadi, + dx x x x ) 2 4 (2 3 5 = c x x x + + 4 4 6326136. + dx x x2 2) 3 ( adalah Jawab : + dx x x2 2) 3 (= [ ] + +2 2 2 2) 3 ( ) 3 )( ( 2 ) ( x x x x dx= + + ) 9 6 (2 3 4x x x dx= c x x x +++++++ + + 1 2 1 3 1 41 291 361 41= c x x x + + +3 4 5392651= c x x x + + +3 4 532351Jadi, + dx x x2 2) 3 ( = c x x x + + +3 4 53235137. 213dx x adalah Jawab :213dx x = 214411]1x= ,_

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4 4) 1 (41) 2 (41= ,_

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) 1 (41) 16 (41= 41416= 415 atau 43318Jadi, 213dx x = 415 atau 43338. +212) 3 ( dx x x adalah Jawab :+212) 3 ( dx x x = 212 323311]1+ x x= ,_

+

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+2 3 2 3) 1 (23) 1 (31) 2 (23) 2 (31= ,_

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+ ) 1 (23) 1 (31) 4 (23) 8 (31= ,_

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1]1

a a [ ] 36 32 4 8412 4 1]1

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+ 0 64 8424aa 0 256 322 4 + a ax 4( )( ) 16 162 2 a a4162aaatau 4162aaJadi, nilai dari a = 4Turunan (Diferensial)47.) (x f = 3x , maka ) ( ' x f = Jawab :) (x f= 3x = 31x) ( ' x f= 131 31x= 333131 x22= 3231 xJadi, ) ( ' x f3231 x48.31 1) (x xx f + , maka ) ( ' x fJawab :31 1) (x xx f + = 3121 + x x1 13121311211 ) ( ' + x x x f = 333122213121 x x = 34233121 x x = 33121x x x x Maka ) ( ' x f33121x x x x 49.21) (

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xx x f , maka ) ( ' x fJawab :21) (

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