Jika diketahui f (×) -f(x-1)=3 dan f(3)=5 maka nilai f (10) adalah

Bab Fungsi Komposisi
Matematika SMA Kelas X

f(x) = ax + b

f(x - 1) = a(x - 1) + b
f(x - 1) = ax - a + b

f(x) - f(x - 1) = 3
ax + b - (ax - a + b) = 3
ax + b - ax + a - b = 3
a = 3

f(x) = ax + b
f(3) = 3a + b = 5
3 . 3 + b = 5
b = 5 - 9
b = -4

f(x) = 3x - 4
f(10) = 3 . 10 - 4
f(10) = 30 - 4
f(10) = 26

Mapel : Matematika
Kelas : X SMA
Bab : Fungsi Komposisi dan Fungsi invers

Pembahasan :
F(x) - f(x - 1) = 3
F(x) = 3 + f(x - 1)
F(3) = 3 + f(2)
5 = 3 + f(2)
F(2) = 2

F(x) = ax + b
F(3) = 3a + b = 5
F(2) = 2a + b = 2
—————————— (-)
a = 3

Substitusi...
2a + b = 2
2(3) + b = 2
b = 2 - 6
b = -4

Maka...
F(x) = ax + b
F(x) = 3x - 4
F(10) = 3(10) - 4
F(10) = 30 - 4
F(10) = 26