c. (fog)⁻¹(p+1) = p + 1/4 1/4 [3(p+1) - 7] = p +1/4........ruas kiri dan kanan dikali 4 3p -4 =4p +1 p = -5
d. (fog)⁻¹ (2p -1) = p -3 1/4[3(2p - 1) - 7 = p - 3.....................ruas kiri dan kanan dikali 4 6p -10 = 4p - 12 2p = -2 p= -1
5. (g⁻¹ o f⁻¹)⁻¹ = f o g ...........................(g⁻¹ o f⁻¹) = (2x -5)/(3x -1) [(2x -5)/(3x -1)]⁻¹ = f o g (x -5) / (3x - 2) = f o g......................f = x-2 f⁻¹ = x +2
f o g = (x -5) / (3x - 2)
f⁻¹o f o g = f⁻¹ o ( fog) g = (x + 2) o [(x - 5)) / (3x - 2)] =[ (x - 5)) / (3x - 2)] + 2 = [( x - 5) + 2 ( 3x -2)] / (3x -2) = (7x - 9)/ (3x - 2)
= (3x-4)o1/4(x-3) = 3.1/4(x-3)-4 = 3/4 x -9/4 -4 =3/4 x -9/4 -16/4
=3/4 x - 25/4
= 1/4 ( 3x -25)
a. (gof)⁻¹(p) = 2
1/4(3p - 25) =2
(3p -25) = 8
3p = 33
p = 11
b. (gof)⁻¹(3)=p -3
1/4(3.3 -25) = p-3
(9 - 25) = 4p - 12
-16 =4p - 12
4p = -4
p= -1
(fog)⁻¹ = g⁻¹o f⁻¹
= 1/4(x -3) o(3x - 4)
= 1/4 [(3x -4) -3]
= 1/4(3x - 7)
c. (fog)⁻¹(p+1) = p + 1/4
1/4 [3(p+1) - 7] = p +1/4........ruas kiri dan kanan dikali 4
3p -4 =4p +1
p = -5
d. (fog)⁻¹ (2p -1) = p -3
1/4[3(2p - 1) - 7 = p - 3.....................ruas kiri dan kanan dikali 4
6p -10 = 4p - 12
2p = -2
p= -1
5. (g⁻¹ o f⁻¹)⁻¹ = f o g ...........................(g⁻¹ o f⁻¹) = (2x -5)/(3x -1)
[(2x -5)/(3x -1)]⁻¹ = f o g
(x -5) / (3x - 2) = f o g......................f = x-2
f⁻¹ = x +2
f o g = (x -5) / (3x - 2)
f⁻¹o f o g = f⁻¹ o ( fog)
g = (x + 2) o [(x - 5)) / (3x - 2)]
=[ (x - 5)) / (3x - 2)] + 2
= [( x - 5) + 2 ( 3x -2)] / (3x -2)
= (7x - 9)/ (3x - 2)