Question

Se considera functia f:R--> R , f(x)= ax+b . Determinati a si b , daca f(1-x)+2f(x) = 2x-7 ,oricare ar fi numarul real x .

Answer 1

a(1-x)+b+2(ax+b)=2x-7
 a-ax+b+2ax+2b=2x-7
ax+a+3b=2x-7, ∀x∈R
atunci \
ax=2x
a+3b=-7

adica
 a=2
a+3b=-7⇒2+3b=-7⇒3b=-9, b=-3


f(x) =2x-3
verificare
2(1-x)-3+2(2x-3)=2-2x-3+4x-6=2x+2-9=2x-7 adevarat. problema este bine rezolvata