Question

Jika f(x - 1) = (x - 1)/ (2 - x) dan f-1 adalah invers dari f maka f-1(x + 1) sama dengan...

Answer 1

Verified answer

Mapel : Matematika
Kelas : X SMA
Bab : Fungsi Komposisi dan Fungsi Invers

Pembahasan :
f(x - 1) = (x - 1)/(2 - x)
f(x - 1) = (x - 1)/[-(x - 1) + 1]
f(x) = x/(-x + 1)

Buat Persamaan
f(x) = y
x/(-x + 1) = y
x = -xy + y
x + xy = y
x(1 + y) = y
x = y/(1 + y)
f¯¹(x) = x/(1 + x)
f¯¹(x + 1) = (x + 1)/(1 + x + 1)
f¯¹(x + 1) = (x + 1)/(x + 2)

Answer 2

Verified answer

Jawaban:
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f(x - 1) = (x - 1)/ (2 - x)
⇒ f(x) = x/(1 - x)
⇒ y = x/(1 - x)
⇒ y - xy = x
⇒ y = x + xy
⇒ y = (1 + y)x
⇒ x = y/ (1 + y)
maka f-1(x) = x/ (1 + x)
⇒ f-1(x + 1) = (x + 1) / (1 + x +1)
⇒ f-1(x + 1) = (x + 1) / (x + 2)

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