Question

Sebuah fungsi dirumuskan
, jika

menyatakan invers fungsi

dan

, nilai

Answer 1

Verified answer

Fungsi invers

jika f(x) = y maka  f⁻¹ (y) = x

f { (5x +4) / (2x-4) } = ³ˣ⁻⁴ log 16
f⁻¹ (³ˣ⁻⁴ log 16) = (5x + 4)/(2x - 4)
f⁻¹ (2p - 1/2) = 6

terdapat persamaan
(i) (5x + 4)/ (2x - 4) = 6 dan (ii) (2p -1/2) = ³ˣ⁻⁴log 16

(i)  (5x + 4) / (2x - 4) = 6
6(2x - 4) = 5x + 4
12x - 24 = 5x + 4
12x - 5x = 4 + 24
7x = 28
x = 4
substitusikan ke (ii)
2p - 1/2 = ³ˣ⁻⁴log 16
2p - 1/2 = ³⁽⁴)⁻⁴log 16
2p - 1/2 = ⁸log 16
2p - 1/2 = ²^³log 2⁴
2p - 1/2 = 4/3 (²log 2)
2p - 1/2 = 4/3
12p - 3 = 8
12p = 11
p = 11/12