Question

F(x) = 2x - 1/x + 4 ; x tidak sama dengan -4
h(x) = -7x + 5/ 4x - 8 ; x tidak sama dengan 2
h(x) = (f o g) invers (x)
berapakah g invers (x) ?

Answer 1

Kompisisi fungsi dan fungsi invers

f(x) = (2x-1)/(x+4)
h(x)= (-7x +5)/(4x-8)
h(x) = fog(x)
g⁻¹(x) = a

f(x) = {fog) o g⁻¹ (x)
(2x-1)/(x+4) = (-7a + 5) / (4a -8)
(-7a + 5)(x+4) = (4a -8)(2x-1)
-7ax - 28 a + 5x + 20 = 8 ax - 4a - 16x + 8
-7ax -8ax -28 a + 4a = -5x - 16x + 8 - 20
-15 ax  - 24 a = -21 x - 12
a (-15x -24) = -21 x -12
a = -(21x +12)/ -(15x + 24)
a = (21x +12)/ (15x +24)
a = 3(7x +4)/ 3(5x +8)
a = (7x + 4)/ (5x + 8)

g⁻¹(x) = (7x + 4)/(5x +8) dengan x ≠ -8/5