Question

Tentukan invers f(x)=3x^2 - 2x + 4

Answer 1

Verified answer

Fungsi
>> Invers

f(x) = 3x² - 2x + 4
y = (√3 x)² - 2x√3/√3 + (1/√3)² + 11/3
y = (√3 x - 1/√3)² + 11/3
(√3 x - 1/√3)² = y - 11/3
√3 x - 1/√3 = ± √(y - 11/3)
√3 x = 1/√3 ± 1/√3 √(3y - 11)
x = 1/3 (1 ± √(3y - 11))

Jadi,
invers dr f(x) = f^-1 (x)
f^-1 (x) = 1/3 (1 ± √(3x - 11))

Answer 2

Verified answer

F(x) = 3x² -2x + 4
f⁻¹ (3x² -2x + 4) = x
3x² -2x + 4 = y
3x² -2x = y - 4
(x² -2/3 x) = 1/3 (y-4)
(x - 1/3)² = 1/3(y-4) + 1/9
(x - 1/3)² = 1/9 { 3(y-4)} + 1}
(x- 1/3) = +_ 1/3 √(3y -12 + 1}
x - 1/3 = +_ 1/3 √(3y -11)
x = 1/3 +- 1/3 √(3y -11)
f ⁻¹(x) = 1/3 { 1  +- √(3x-11)}