Question

Jika (f o g) =4x^2 + 8x -3 dan g(x) = 2x + 4, maka f^-1 (x) adalah

Answer 1

Fog(x) = 4x² +8x - 3
f(2x+4)= 4x² +8x - 3
2x+4 = y
x = 1/2(y-4)
f(y) = 4 {1/2 (y-4)}² + 8{ 1/2(y-4)} - 3
f(y)= 4(1/4 (y²-8y+16)) + 4(y-4) - 3
f(y) = y² -8y + 16 +4y -16 - 3
f(y) = y² - 4y - 3
f(x) = x² -4x - 3

f⁻¹(x²-4x-3) = x
x²-4x-3 = y
x²-4x = y+3
(x-2)² = y+3+4
x-2 = √(y+7)
x = 2 +√(y+7)
f⁻¹(x) = 2 + √(x+7)
..