Question

F(2x+3) =
x+3
------
2x-4
maka f(x) -1 ???

Answer 1

Verified answer

Materi : Fungsi Komposisi dan Fungsi Invers

Pembahasan :
f(2x + 3) = (x + 3)/(2x - 4)

Misal 2x + 3 = a —» x = (a - 3)/2

Substitusi...
f(a) = [(a - 3)/2 + 3]/[(a - 3) - 4]
f(a) = [(a - 3 + 6]/2]/(a - 7)
f(a) = (a + 3)/(2a - 14)
f(x) = (x + 3)/(2x - 14)

Buat f(x) = y,
(x + 3)/(2x - 14) = y
x + 3 = 2xy - 14y
2xy - x = 3 + 14y
x(2y - 1) = 3 + 14y
x = (14y + 3)/(2y - 1)
f¯¹(x) = (14x + 3)/(2x - 1)