Jika diketahui f(x) = x + 1 dan g(x) = 3x^2 + x +3. Persamaan (fog)^-1 (x)

jawab

f(x) = x + 1
g(x)= 3x² + x + 3

fog(x)= 3x²+ x + 3 + 1
fog(x) = 3x² +x + 4
3x² +x = y  - 4
x² + 1/3 x = 1/3 (y - 4)
(x + 1/6)² = 1/3 y - 4/3 + 1/36
(x + 1/6)² = 1/3 y - 47/36
(x + 1/6)² = 1/36 (12 y - 47)

x + 1/6 = 1/6 (√(12y - 47))
x = -1/6 +- 1/6 (√12y -47))
x = -1/6 ( 1 +- (√(12y - 47))

(fog)⁻¹(x) =  -1/6 ( 1 +- (√(12x - 47))