Question

sa se determine functia de gradul 1 f:R>R, astfel incit 2xf(x)+3xf(1-x)=4x-1

dau 30 pcte

Answer 1

f(x)=ax+b ,a≠0
2xf(x)+3xf(1-x)=4x-1
2(ax+b)+3[a(1-x)+b]=4x-1
2ax+2b+3a-3ax+3b=4x-1
-ax+3a+5b=2x-1⇒

-ax=2x⇒a=-2
3a+5b=-1
-6+5b=-1
5b=5
b=1
Atunci functia care indeplineste conditia este de forma
f(x)=-x+1