Jika f(x) = 2x-3 / x-1, maka turunan dari f^-1(x) =…

Jawab:
1/(x²-4x+4)

Penjelasan dengan langkah-langkah:

Diketahui
f(x) = (2x-3)/(x-1) -> x ≠ 1

Dicari
(f⁻¹(x))'

f(x) = 2x-3 / x-1
y = 2x-3 / x-1
x = 2y-3 / y-1
2y-3 = x(y-1)
2y-3 = xy-x
2y-xy = 3-x
y(2-x) = 3-x
y = (3-x)/(2-x) -> x ≠ 2
f⁻¹(x) = (3-x)/(2-x)

Lalu cari turunannya
u = 3-x, v = 2-x
(u/v)' = (u'v-uv')/v²
((3-x)/(2-x))' =
((3-x)'(2-x)-(3-x)(2-x)')/(2-x)²
(-(2-x)-(-(3-x)))/(2-x)(2-x) =
(-2+x+3-x)/(4-2x-2x+x²) =
1/(x²-4x+4)

<(7o7)>