Penjelasan dengan langkah-langkah:
NOMOR 6
f^-1 (x) = 2x + 5
g^-1 (x) = x + 2
(g o f)^-1 (1) = ...
(g o f)^-1 (x) = 2x + 5 + 2
(g o f)^-1 (x) = 2x + 7
(g o f)^-1 (1) = 2(1) + 7 = 9
NOMOR 7
g(x) = (5x+2)/(3x-2)
g^-1 (a) = -2
y = (5x+2)/(3x-2)
y(3x-2) = 5x + 2
3xy - 2y = 5x + 2
3xy - 5x = 2y + 2
x(3y - 5) = 2y + 2
x = (2y+2)/(3y-5)
g^-1 (x) = (2x+2)/(3x-5)
g^-1 (a) = (2a+2)/(3a-5)
-2 = (2a+2)/(3a-5)
-6a + 10 = 2a + 2
-6a - 2a = -10 + 2
-8a = -8
a = 1
NOMOR 8
g(x-2) = (x-4)/(x+2)
f(x) = x² + 3
(f o g^-1)(2) = ...
g(x-2) = (x-4)/(x+2)
Pemisalan :
x - 2 = p
x = p + 2
g(p) = (p+2-4)/(p+2+2)
g(p) = (p-2)/(p+4)
g(x) = (x-2)/(x+4)
y = (x-2)/(x+4)
xy + 4y = x - 2
xy - x = -4y - 2
x(y - 1) = -4y - 2
x = (-4y-2)/(y-1)
g^-1(x) = (-4x-2)/(x-1)
(f o g^-1)(x) = ((-4x-2)/(x-1))² + 3
(f o g^-1)(2) = ((-4(2)-2)/(2-1))² + 3
(f o g^-1)(2) = ((-8-2)/1)² + 3
(f o g^-1)(2) = (-10/1)² + 3
(f o g^-1)(2) = 100 + 3 = 103
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