Question

F={(1,5)(2,6)(3,-1)(4,8)}
G={(2,-1)(1,2)(5,3)(6,7)}

Tentukanlah
a).(g•f)(x)
b).(f•g)(x)

Tolong dijawab yaaa

Answer 1

F={(1,5)(2,6)(3,-1)(4,8)}

G={(2,-1)(1,2)(5,3)(6,7)}

Tentukanlah
a).(g•f)(x)
b).(f•g)(x)

Tolong dijawab yaaa

JAWAB

a). (g•f)(x) = g(f(x))
maka
◆g(f(1)) = g(5) = 3
◆g(f(2)) = g(6) = 7

sehingga
(g•f)(1) = 3
(g•f)(2) = 7

Misalkan (g•f)(x) = ax + b, maka
a.(1) + b = 3
a.(2) + b = 7
------------------ -
⇨ -a = -4
⇨ a = 4
untuk mendapat b maka
a + b = 3 → b = 3-4 = -1

Jadi nilai
(g•f)(x) = ax + b = 4x - 1


b). (f•g)(x) = f(g(x))
maka
◆f(g(1)) = f(2) = 6
◆f(g(5)) = f(3) = -1
sehingga
(f • g)(1) = 6
(f • g)(5) = -1

Misalkan (f•g)(x) = ax + b, maka
a.(1) + b = 6
a.(5) + b = -1
------------------ -
⇨ -4a = 7
⇨ a = -7/4
untuk mendapat b maka
a + b = 6 → b = 6 - (7/4) = 17/4
Sehingga nilai
(f•g)(x) = ax + b = (-7/4)x + (17/4) = ¼ (17 - 7x)