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12.85 funkcja liniowa

1285 Funkcja Liniowa class=

Odpowiedź :

(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