Page 36 - 4. UKBM MAT WA

Untuk mendapatkan inversnya

−
3 2x
y =
x − 1
−
 ..... ..... 3 2x
= −
=
 ..... ..... ..... 3
+
+
+
 ..... (..... ..... = +
) ..... 3
+
..... .....
 ..... =
+
..... .....
+
..... .....
 h − 1 ( ) y =
+
..... .....
+
 h − 1 ( ) x = ..... .....
+
..... .....
+
 (..... ..... ) ( ) = − 1 ..... ..... .....
+
..... .....
Cara II : Terlebih dahulu mencari invers dari masing-masing fungsi, baru
kemudian dikomposisikan
1
f ( ) x =
x − 1
1 − 1
..... = ( g f ) ( ) x
x − 1 )( )
−
 ..... (..... ..... = g ( ) x = x − 2 = (....... ....... x
) 1
( ))
=
 ..... ..... 1  .... x − 2 = ....... (....... x
=
−
+
=
 ..... ..... 1  = ..... 2 ....... (.......... )
x
+
=
( ) ..... 2
+
..... 1  ....... y = + ...............
 ..... = =
.....  ....... x = + ..........
( ) ..... 2
+
..... 1 ..........
 ....... ( ) y = =
..... ..........
+
..... 1
 ....... ( ) x =
.....
)
−
1
Jadi invers dari (g f adalah (..... ..... ) ( ) x = ..........
..........

−
1
x =
2. Diketahui fungsi f − 1 ( ) 3x + 4 dan g − 1 ( ) x = 2x . Tentukanlah ( f g ) ( ) 2 !

Jawab:
− 1
( f g ) ( ) 2
)( )
= (....... ....... 2
= ....... (....... 2
( ))
( )
= ....... ...
= .....

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