Question

G(x) = 4x – 1 dan (f○g)(x) = 8x – 1 maka f^-1 (-5)(x) = ...
A. 0
B. -1
C. -2
D. -3
E. -4

Answer 1

G(x) = 4x -1
  y    = 4x - 1
y + 1 = 4x
y+1 / 4 = x
g⁻¹(x) = x + 1/ 4
maka nilai f(x)
f(x) = fog o g⁻¹
      = 8 ( x-1 )/4) -1
      = 2 ( x-1) -1
      = 2x -2-1
      = 2x -3
 y   = 2x -3
y + 3 = 2x
y +3/2 = x
maka nilai dari 
f⁻¹(-5) = -5 + 3/2
         = -2/2
         = -1

Answer 2

G^-1 = 4x-1 = y
         =4x = y +1
  g^-1 = x  = y+1/4
fog = 8x-1
f = 8 (x+1/4) - 1
f = 8x/4 + 8/4 - 1
f = 2x + 1
f^-1 = 2x + 1 =y
        x = y/2 - 1/2
f^-1 (5) = -5/2 - 1/2         
             = -6/2
             = -3