sertai langkah pengerjaan
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Penjelasan dengan langkah-langkah:
FUNGSI KOMPOSISI INVERS
f(x) = 2x – 5
x + 3
g(x) = 3x + 1
(f o g)(x) = f(3x + 1)
(f o g)(x) = 2(3x + 1) – 5
3x + 1 + 3
(f o g)(x) = 6x – 3
3x + 4
misal : (f o g)(x) = y
y = 6x – 3
3x + 4
y(3x + 4) = 6x – 3
3xy + 4y = 6x – 3
3xy – 6x = –4y – 3
x(3y – 6) = –4y – 3
x = –4y – 3
3y – 6
(f o g)-¹(x) = –4x – 3
3x – 6
(f o g)-¹(3) = –4(3) – 3
3(3) – 6
(f o g)-¹(3) = –12 – 3
9 – 6
(f o g)-¹(3) = – 15
3
(f o g)-¹(3) = –5 ✔
Penyelesaian
f(x)=2x-5/x+3
g(x)=3x+1
--------------------
f(g(x))
=2(3x+1)-5/3x+1+3
=6x-3/3x+4
----------------------------------------
(f o g)‾¹(x)
y=6x-3/3x+4
3xy+4y=6x-3
3xy-6x=-4y-3
x(3y-6)=-4y-3
x=-4y-3/3y-6
(f o g)‾¹(x)=-4x-3/3x-6
----------------------------------------
(f o g)‾¹(3)
=-4(3)-3/3(3)-6
=-12-3/9-6
=-15/3
=-5