The document involves calculating inverse functions of various compositions of functions f(x) and g(x). It provides the definitions of f(x) and g(x) and calculates: 1) The inverse functions f^-1(x) and g^-1(x) 2) The compositions (f o g)(x), (g o f)(x), and their inverse functions 3) The inverse functions of (f o g)^-1(x) and (g o f)^-1(x) 4) Confirms the relationship that (f o g)^-1(x) = (g^-1 o f^-1)(x) and (g o f)^-1

1. 1. Diketahui:
f(x) = 4x + 3
g(x) = 3x – 2
Tentukanlah:
a. f-1(x)
 f(x) = 4x + 3
 y = f(x)
 y = 4x + 3
 y – 3 = 4x

4
3

y
x
 )(1
yfx 


4
3
)(1 
 y
yf

4
3
)(1 
 x
xf
b. g-1(x)
y = g(x)
 y = 3x – 2
 y + 2 = 3x

3
2

y
x

3
2
)(1 
 y
yg

3
2
)(1 
 x
xg
c. (f o g)(x) = f(g(x))
= f(3x – 2)
= 4(3x – 2) + 3
= 12x – 8 + 3
= 12x – 5
d. (g o f)(x) = g(f(x)
= g(4x + 3)
= 3(4x +3) – 2
= 12x + 9 – 2
= 12x + 7
e. Jika (f o g)(x) = h(x), tentukanlah h-1(x)
h(x) = 12x – 5
y = 12x – 5
12
5

y
x
12
5
)(1 
 y
yh
12
5
)(1 
 x
xh

2. f. Jika (g o f)(x) = p(x), tentukanlah p-1(x)
p(x) = 12x + 7
y = 12x + 7
12
7

y
x
12
7
)(1 
 y
yp
12
7
)(1 
 x
xp
g. (f-1 o g-1)(x) = f-1(g-1(x))
= 




 
3
21 x
f
=
4
3
3
2





 x
=
4
3
92





 x
(f-1 o g-1)(x) =
12
7x
12
7
)(1 
 x
xp
h. (g-1 o f-1)(x) = g-1 ((f-1(x))
= 




 
4
31 x
g
=
3
2
4
3





 x
=
3
4
83





 x
(g-1 o f-1)(x) =
12
5x
12
5
)(1 
 x
xh
(f-1 o g-1)(x) = (g o f)-1(x)
(g-1 o f-1)(x) = (f o g)-1(x)

3. 2. Diketahui:
f(x) = 3x + 1
g(x) = -2x + 5
tentukanlah:
a. (f o g)-1(x) = (g-1 o f-1)(x)
f(x) = 3x + 1 g(x) = -2x + 5
y = f(x) = 3x + 1 y = g(x) = -2x + 5
y = 3x + 1 y = -2x + 5
3
1
)(1 
 x
xf
2
5
)(1 
 x
xg
(f o g)-1(x) = (g-1 o f-1)(x)
= g-1 (f-1(x))
= 




 
3
11 x
g
=
2
5
3
1





 

x
=
2
3
151 x
=
6
16 x
b. (g o f)-1(x) = (f-1 o g-1)(x)
(f o g)-1(x) = (g-1 o f-1)(x)
(g o f)-1(x) = (f-1 o g-1)(x)
3. Diketahui:
(f o g)(x) = 2x + 3
f(x) = 3x + 1
tentukanlah g(x)!
Jawab:
(f o g)(x) = 2x + 3
f (g(x)) = 2x + 3
3.g(x) + 1 = 2x + 3
3.g(x) = 2x + 2
3
22
)(


x
xg
4. Diketahui :
(f o g)-1(x) = 5x + 4
g(x) =
3
12 x
Tentukanlah f(x)!