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Kelas : X SMAmapel : matematika
kategori : fungsi
kata kunci : fungsi invers
kode : 10.2.6 [matematika SMA kelas 10 Bab 6 fungsi]
Pembahasan:
f(x) = (1 - 5x) / (x + 2) , dengan x ≠ -2
ditanya f^-1(x) = ...?
jawab:
(1 - 5x) / (x + 2) = y
(1 - 5x) = y (x + 2)
1 - 5x = xy + 2y
-5x - xy = 2y - 1
x (-5 -y) = (2y -1)
x = (2y -1) / (-y -5)
jadi f^-1(x) = (2x -1) / (-x -5) dan x ≠ -5
atau
y = (1 - 5x) / (x + 2)
y (x + 2) = (1 - 5x)
xy + 2y = 1 - 5x
xy + 5x = 1 - 2y
x (y + 5) = 1 - 2y
x = (1 -2y) / (y + 5)
f^-1(x) = (1 - 2x) / (x + 5) , dan x ≠ -5
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