Question

Se considera functia: f:R->R;f(x-2)=3x-4.
a)Sa se determine functia.
b)Sa se rezolve ecuatia f(2x+1)-2f(x)=5

Answer 1

f(x - 2) = 3x - 4 => f(x) = 3x + 2

f(2x + 1) - 2f(x) = 5

f(2x + 1) = 3(2x + 1) + 2 = 6x + 3 + 2 = 6x + 5

2f(x) = 2(3x + 2) = 6x + 4

f(2x + 1) - 2f(x) = 5 ⇔ 6x + 5 - (6x + 4) = 6x + 5 - 6x - 4 = 1