Mohon Kali atas pertolongannya..tolong jawab Isi beserta jalannya ,terimakasih ...

40.

f(x) = x² + 4x + 1
f⁻¹ (x² + 4x +1) = x
x² + 4x + 1= y
x² + 4x = y-1
(x+2)² = y - 1 + 4
(x + 2) =  √(y+3)
x = - 2 +√(y+3)
f⁻¹ (x) = - 2 + √(x+3)

fog(x) =9x² -54x  + 78
g(x) = f⁻¹ o { fog)(x)
g(x) = -2 + - √(9x ²- 54x +78+3)
g(x) = - 2 +- √(3x - 9)²
g(x) = - 2 +- (3x -9)
g(x) = -2 + 3x - 9 atau g(x) = 3x -11
g(x) = -2 - 3x +9  atau g(x) = - 3x + 7
g(1) = - 8 --> g(x) = 3x - 11
g(-1) = 3(-1) - 11
g(-1) = -14

Cara lainnya, biar lebih berwarna.

(fog)(x) = f(g(x))
= (g(x))^2 + 4(g(x)) + 1

(g(x))^2 + 4(g(x)) + 1 = 9x^2 - 54x + 78
(g(x))^2 + 4g(x)) = 9x^2 - 54x + 77
g(-1)^2 + 4g(-1) = 9(-1)^2 - 54(-1) + 77
g(-1)^2 + 4g(-1) = 9 + 54 + 77
g(-1)^2 + 4g(-1) = 140
g(-1)^2 + 4g(-1) - 140 = 0

misal, g(-1) = z
z^2 + 4z - 140 = 0
(z - 10)(z + 14) = 0
z = 10 atau z = -14

g(-1) = -14