Question

Diketahui f(x) = (5x - 3)/(x - 2), x = (tidak sama dengan) 3. Jika f ^-1 adalah fungsi invers dari f, tentukan rumus untuk f^- 1(x - 3)!​

Answer 1

Penjelasan dengan langkah-langkah:

f(x) = (5x - 3)/(x - 2)

y = (5x - 3)/(x - 2)

y(x-2) = 5x-3

xy - 2y = 5x - 3

3 - 2y = 5x - xy

3 - 2y = x(5 - y)

(3 - 2y)/(5 - y) = x

f^-1(x) = (3 - 2x)/(5 - x)

f^-1(x - 3) = (3 - 2(x - 3))/(5 - (x - 3))

f^-1(x - 3) = (3 - 2x + 6)/(5 - x - 3)

f^-1(x - 3) = (9 - 2x)/(2 - x)