Question

TENTUKAN INVERS FUNGSINYA
F(x) = 2/3x-1 - 3/6x-2,x tidak = 1/3
Sama cara ya..

Answer 1

F(x) = 2/(3x-1)  - 3/(6x-2) ; x ≠ 1/3

f(x) = 4/(6x-2) - 3/(6x-2)
f(x) = 1/(6x-2)

cari invers:
         y = 1/(6x-2)
y(6x-2) = 1
 6xy-2y = 1
      6xy = 1 +2y
          x = (1+2y)/6y

f⁻¹(x) = (1+2x)/6x  ; x ≠ 0

Answer 2

Dik:
F(x) = 2/3x-1 - 3/6x-2
x tidak = 1/3
y=f(x)

Maka:
y= 2/(3x - 1) - 3/(6x - 2)
y= 2/(3x - 1) . 2/2 - 3/(6x - 2)
y= 4/(6x - 2) - 3/(6x - 2)
y = 1/(6x - 2)
Maka:
y = 1/(6x - 2)
6xy - 2y = 1 pindah ruas
6xy = 1+2y
x = (2y + 1) dibagi dengan 6y
Karena yg ditanya invers maka variable y berubah jadi x/kebalikannya
Sehingga:
f^-1(x) = (2x + 1)
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6x
Terima kasih