Question

Fie a,b ∈R. Aratati ca functia f :R→ R, f(x)=ax-b are proprietatea:

f de ((x+y)/2)=( f(x)+ f(y))/2, pentru oricare x, y ∈R

Answer 1

f ((x+y)/2)=a·(x+y)/2-b=(ax+ay-2b)/2
( f(x)+ f(y))/2=(ax-b+ay-b)/2=(ax+ay-2b)/2⇒
f ((x+y)/2)=( f(x)+ f(y))/2