Fungsi f: R➡R ditentukan oleh f(x)=2x+1 per x-3 untuk x ≠ 3 . Jika f–¹ adalah fungsi invers dari f, rumus fungsi f–¹(x-2)=......

jawab

f(x)= (2x + 1)/(x-3)

f⁻¹ {(2x+1)/(x-3)} = x

(2x+1)/(x-3) =y
2x +1 = y(x-3)
2x + 1 = xy - 3y
2x - xy = - 3y - 1
x(2 - y) = (-3y -1)
x = (-3y -1)/(2-y)
x= (3y+1)/(y -2)

f⁻¹(x) = (3x +1)/(x-2)
f⁻¹(x-2) = {(3(x-2) +1} / (x-2 -2)
f⁻¹(x-2) = (3x - 5)/(x - 4)