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# Ppt fungsi komposisi

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### Ppt fungsi komposisi

1. 1. REMEMBER Diketahui : f : R R , dengan : f ( x ) x2 5x 6 f (1) 12 5(1) 6 2 f(a) a 2 5a 6 2 f ( x 1 ) ( x 1) 5( x 1) 6 x2 2 x 1 5x 5 6 x2 7 x 12
2. 2. FUNGSI KOMPOSISI A f B g C x y z h =g f Diketahui : f ( x) y , g ( y) z , h( x) ( g  f )(x) zKarena g ( y ) z dan f ( x) y , maka : g ( y) g ( f ( x)) z Karena ( g  f )(x) z dan g ( f ( x)) z , maka : Teorema ( g  f )(x) g ( f ( x))
3. 3. Fungsi : ( g  f )(x) g ( f ( x)) disebut fungsi komposisi atau fungsi majemuk. SIFAT-SIFAT FUNGSI KOMPOSISI 1. ( f  g )(x) ( g  f )(x) 2. ( f  ( g  h))(x) (( f  g )  h)(x)
4. 4. CONTOH 2 5x Diketahui : f ( x ) 2 x 3 , g( x ) x 1 , dan h( x ) x 2 Tentukan : A . ( f  g )( x) C. (h  f )(1) E. ( f  h  g )( 1) B. ( g  f )(x) D. (h  f  g )(x) JAWABA . ( f  g )( x) f ( g ( x)) B . ( g  f )( x) g ( f ( x)) 2 g (2 x 3) f (x 1) (2 x 3)2 1 2( x 2 1) 3 ( 4 x 2 12 x 9) 1 2 x2 1 4 x 2 12 x 8
5. 5. CONTOH 2 5x Diketahui : f ( x ) 2 x 3 , g( x ) x 1 , dan h( x ) x 2 Tentukan : A . ( f  g )( x) C. (h  f )(1) E. ( f  h  g )( 1) B. ( g  f )(x) D. (h  f  g )(x) JAWABC . (h  f )(1) h( f (1)) D . (h  f  g )(x) (h  f )(g ( x)) h(2. 1 3) (h  f )( x 2 1) h( f ( x 2 1)) 5(1) 5( 2 x 2 1) h( 2 x 2 1) ( 2 x 2 1) 2 1 2 5 10 x 2 5 3 2 x2 3
6. 6. CONTOH 2 5xDiketahui : f ( x ) 2 x 3 , g( x ) x 1 , dan h( x ) x 2Tentukan : A . ( f  g )( x) C. (h  f )(1) E. ( f  h  g )( 1) B. ( g  f )(x) D. (h  f  g )(x)JAWAB E . ( f  h  g )( 1) ( f  h)( g ( 1)) f 0 ( f  h )(( 1)2 1) 2.0 3 3 f (h(0)) 5(0) f 0 2