Jawab no 3,4,5 dengan penjelasan

Matematika (Fungsi Invers)

Nomor 3
f(x) = x² - 5x + 2
y = x² - 5x + 2
y + 17/4 = x² - 5x + 2 + 17/4
y + 17/4 = x² - 5x + 25/4
y + 17/4 = (x - 5/2)²
x - 5/2 = ±√(y + 17/4)
x = ±√(y + 17/4) + 5/2

f`¹(x) = √(x + 17/4) + 5/2
f`¹(x) = (-√(x + 17/4)) + 5/2

Nomor 4
f(x) = 2x² + 6x - 1
y = 2x² + 6x - 1
y/2 = x² + 3x - ½
y/2 + 11/4 = x² + 3x - ½ + 11/4
y/2 + 11/4 = x² + 3x + 9/4
(2y + 11) / 4 = (x + 3/2)²
±√(2y + 11) = 2(x + 3/2)
2x + 3 = ±√(2y + 11)
x = ±(√(2y + 11) - 3) / 2

f`¹(x) = (√(2x + 11) - 3) / 2
f`¹(x) = ((-√(2x + 11)) - 3) /2

Nomor 5
f(x) = (x - 7) / (3x + 2)
y (3x + 2) = x - 7
3xy + 2y = x - 7
x - 3xy = 2y + 7
x(1 - 3y) = (2y + 7)
x = (2y + 7) / (1 - 3y)

f`¹(x) = (2x + 7) / (1 - 3x)