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Similar to Invers fungsi (20)
Invers fungsi
- 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
7x
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
5x
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)!