dik:f(x)=2x+3 dan (fog) (x+1)=-2x²-4x-1.tentukanlah g-¹(x) dan g¹(-2)

Materi : Fungsi Komposisi

(fog)(x+1) = -2x²-4x-1
f(g(x+1)) = -2x²-4x-1
2(g(x+1)) + 3 = -2x²-4x-1
2(g(x+1)) = -2x²-4x-4
g(x+1) = -x²-2x-2

misal x+1 = a ----> x=a-1
g(a) = -(a-1)²-2(a-1)-2
g(a) = -a²+2a-1 -2a+2-2
g(a) = -a² -1
g(x) = -x²-1

y= -x²-1
-x²= y+1
x²= -y-1
x= √(-y-1)

jadi g-¹(x) = √(-x-1)
g-¹(-2) = √(-(-2)-1)= √1 = 1

semoga membantu