Diketahui f(x)=1/2 x+4 dan g(x)=1/3 x-2. Nilai dari

42

Pembahasan

Diketahui fungsi f(x) = 1/2 x + 4 dan g(x) = 1/3 x - 2.
Kita perlu mencari nilai f(2) + g(9) - (fog)^-1(-3).

1. Hitung f(2):
f(2) = 1/2 * 2 + 4 = 1 + 4 = 5

2. Hitung g(9):
g(9) = 1/3 * 9 - 2 = 3 - 2 = 1

3. Cari fungsi komposisi (fog)(x):
(fog)(x) = f(g(x)) = f(1/3 x - 2)
           = 1/2 * (1/3 x - 2) + 4
           = 1/6 x - 1 + 4
           = 1/6 x + 3

4. Cari invers dari fungsi komposisi (fog)^-1(x):
Misalkan y = 1/6 x + 3
y - 3 = 1/6 x
x = 6(y - 3)
x = 6y - 18
Jadi, (fog)^-1(x) = 6x - 18

5. Hitung (fog)^-1(-3):
(fog)^-1(-3) = 6*(-3) - 18 = -18 - 18 = -36

6. Hitung nilai akhir:
f(2) + g(9) - (fog)^-1(-3) = 5 + 1 - (-36)
                               = 6 + 36
                               = 42