jika diketahui f(x)-f(x-1)=3 dan f(3)=5,maka nilai f(10)=

Bab Fungsi
Matematika SMP Kelas VIII

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
a = 3

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

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

Matematika X SMA
→→ Fungsi ←←

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

f(4) = 3 + f(3)
f(4) = 3 + 5
f(4) = 8

Membentuk suatu barisan...
f(2) , f(3) , f(4) , ...
2 , 5 , 8

Un = 3n - 1
f(10) = 3(9) - 1
f(10) = 27 - 1
f(10) = 26