diketahui fungsi f(x)= 5x+3/2x-1 , x ≠ 1/2 dan g(x)= 3x+2. tentukan hasil dari : a.( f-¹og)(x). b.(fog-¹)(x). c. (f-¹og-¹)(x)

Dik :
f(x) = (5x + 3) / (2x - 1)
y = (5x + 3) / (2x - 1)
y(2x -1) = 5x + 3
2xy - y = 5x + 3
2xy - 5x = y + 3
x (2y - 5) = y + 3
x = (y + 3) / (2y - 5)
f-1(x) = (x + 3) / (2x - 5)

g(x) = 3x + 2
y = 3x + 2
3x = y - 2
x = (y - 2) / 3
g-1(x) = (x - 2) /3

a. (f-1og)(x) = f-1(3x + 2)
= ((3x + 2) + 3) / (2(3x + 2) - 5)
= (3x + 2 + 3) / (6x + 4 - 5)
= (3x + 5) / (6x - 1)

b. (fog-1)(x) = f ((x-2) / 3)
= (5((x - 2) / 3) + 3) / (2((x - 2) / 3) - 1)
= ((5x - 10) / 3) + 9/3) / ((2x - 4) / 3) - 3/3)
= ((5x - 1) / 3) / ((2x - 7) / 3)
= ((5x - 1) / 3) x (3 / (2x - 7))
= (5x - 1) / (2x - 7)

c. (f-1og-1)(x) = f-1((x - 2) / 3)
= ( ((x - 2) / 3) + 3 ) / (2( (x - 2) / 3 ) + 5)
= ( ((x - 2) / 3) + 9/3) / ( (2x - 4) / 3 ) + 15/3 )
= ( (x + 7) / 3 ) / ( (2x - 11) / 3 )
= ( (x + 7) / 3 ) x ( 3 / (2x - 11) )
= (x +7) / (2x - 11)

Semoga membantu.