nomor 1) f(x) = x(pangkat 2) dan (f ° g)(x) = x ( pangkat 2) - 2x + 1 maka g(3) adalah nomor 2) f(x) = x+2 dan g(x)= 3x(pangkat 2)+ 4x+1 maka (g°f) (x)= nomor 3

1.]
f(x) = x²
f(g(x)) = x² - 2x + 1
(g(x))² = (x - 1)²
g(x) = x - 1

➙ g(3) = 3 - 1 = 2

2.]
f(x) = x + 2
g(x) = 3x² + 4x + 1

➙ g(f(x)) = g(x + 2)
= 3(x + 2)² + 4(x + 2) + 1
= 3x² + 12x + 12 + 4x + 8 + 1
= 3x² + 16x + 21

3.]
f(x) = (2x + 1) / (x + 5)
y = (2x + 1) / (x + 5)
xy + 5y = 2x + 1
xy - 2x = 1 - 5y
x(y - 2) = 1 - 5y
x = (1 - 5y) / (y - 2)
➙ f⁻¹(x) = (1 - 5x) / (x - 2)

4.]
f(x) = 7x - 2
y = 7x - 2
x = (y + 2) / 7
f⁻¹(x) = (x + 2) / 7
➙ f⁻¹(x + 1) = (x + 3) / 7

5.]
f(x) = 1 / (x + 1)
y = 1 / (x + 1)
xy + y = 1
xy = 1 - y
x = (1 - y) / y
f⁻¹(x) = (1 - x) / x
-5 = (1 - x) / x
-5x = 1 - x
-4x = 1
➙ x = - ¼

6.]
f(3x - 5) = 7x + 2

Misal 3x - 5 = u
Maka x = (u + 5) / 3

Jadi
f(u) = [tex] 7 ( \frac{u + 5}{3} ) + 2 [/tex]
f(x) = [tex] 7 ( \frac{x + 5}{3} ) + \frac63 [/tex]
f(x) = [tex] (\frac{7x + 35 + 6}{3} ) [/tex]
f(x) = [tex] \frac{7x + 41}{3} [/tex]
y = (7x + 41) / 3
3y = 7x + 41
7x = 3y - 41
x = (3y - 41) / 7
➙ f⁻¹(x) = (3x + 41) / 7

7.]
f(x) = x + 3
g(x) = 2x + 4

g(f(x)) = g(x + 3)
= 2(x + 3) + 4
= 2x + 10

y = 2x + 10
y - 10 = 2x
x = (y - 10) / 2
(g o f)⁻¹(x) = (x - 10) / 2
(g o f)⁻¹(2) = (2 - 10) / 2
➙ (g o f)⁻¹(2) = -4

8.]
f(x) = 5²ˣ
y = 5²ˣ
⁵log y = 2x
x = (⁵log y) / 2
➙ f⁻¹(x) = (⁵log x) / 2

9.]
f⁻¹(x + 1) = 3x - 5
f⁻¹(x) = 3(x - 1) - 5
➙ f⁻¹(x) = 3x - 8

10.]
f(x) = 3 - x³
g(x) = 1 / (x + 5)
g(f(x)) = g(3 - x³)
= 1 / (3 - x³ + 5)
= 1 / (8 - x³)

y = 1 / (8 - x³)
8y - x³y = 1
x³y = 8y - 1
x³ = (8y - 1) / y
x = ∛ [ (8y - 1) / y ]
(g o f)⁻¹(x) = ∛ [ (8x - 1) / x ]
(g o f)⁻¹(⅐) = ∛ [ (8 • ⅐ - 1) / ⅐ ]
➙ (g o f)⁻¹(⅐) = ∛ 1
= 1

11.]
f(x) = 1 + 1/x
g(x) = 2x - 4
(f⁻¹ o g⁻¹)(x) bentuk yang lainnya yaitu
(g o f)⁻¹(x)

Cari (g o f)(x) dlu
g(f(x)) = g(1 + 1/x)
= 2(1 + 1/x) - 4
= 2 + 2/x - 4
= 2/x - 2

y = 2/x - 2
2/x = y + 2
x = 2 / (y + 2)
➙ (g o f)⁻¹ = 2 / (x + 2)