12.85 funkcja liniowa

(1)a3x+b=3(ax+b)+10∧(2)a(x+3)+b=ax+b+12
(1):
3ax+b = 3ax+3b+10
b=3b+10
b=-5
(2):
ax+3a+b=ax+b+12
3a+b=b+12
a=4
czyli:
y=4x-5
Odpowiedź:
f(x) = ax+ b
f(3x) = 3f(x)+ 10 ∧ f(x +3) = f(x) + 12
f(3x) = a * 3x + b = 3ax + b
3f(x) + 10 = 3 * ax + 3b + 10 = 3ax + 3b + 10
f(x + 3) = a(x + 3) + b
f(x) + 12 = ax + b + 12
3ax + b = 3ax + 3b + 10
3ax - 3ax + b - 3b = 10
- 2b = 10
2b = - 10
b = - 10/2 = - 5
a(x + 3) + b = ax + b + 12
ax + 3a - 5 = ax - 5 + 12
ax - ax + 3a = 5 - 5 + 12
3a = 12
a = 12/3 = 4
y = 4x - 5