Question

Fie relatia 2f(x) + 3f(-x) = modul(x) + x. Sa se afle f(x). Multumesc!

Answer 1

2f(x) + 3f(-x) = |x| + x  [1]
Inclocuim in egalitatea de mai su pe x cu -x si obtinem:
2f(-x)+3f(x)=|-x|-x
2f(-x)=|-x|-x-3f(x)
f(-x)=[|-x|-x-3f(x)]/2 si inlocuim in [1].
2f(x)+3*[|-x|-x-3f(x)]/2=|x| + x
2f(x)+3/2*|-x|-3/2*x-9/2*f(x)=|x|+x
f(x)*(2-9/2)=|x|+x-3/2*|-x|+3/2*x
f(x)*(-5/2)=|x|+5/2*x-3/2*|-x|
f(x)=(-2/5)*[|x|+5/2*x-3/2*|-x|]
f(x)=-2/5*|x|-x+3/5*|-x|