Diketahui fungsi f(x) = 2x + 1 dan (f ○ g)(x + 1) = -2x^2 – 4x – 1. Tentukanlah g^-1(x) dan g^-1(-2)!

jawab
f(x)= 2x + 1
fog(x+1) = - 2x² - 4x - 1
f { g(x+1)}= -2x² -4x - 1
2.g(x+1) + 1= -2x²-4x -1
2. g(x+1) = -2x² - 4x - 2
2. g(x+1) = 2(-x² -2x -1)
g(x+1) = - x²- 2x - 1
g(x+1) = - (x² + 2x + 1) = - (x +1)²
g(x) = - x²

g⁻¹(-x²) = x
-x² = y
x²  = -y
x = √(-y)
g⁻¹(x) = √(-x)
g⁻¹(-2) = √{-(-2)} = √2