verifici daca ecuatia f(x)=y admite solutii , unde y∈(0 ,∞)
y=(1-x)/(1+x)
y+xy=1-x=>
x=(1-y)/(1+y)
Vom arata ca -1<(1-y)/(1+y)<1 , adica x∈(-1 ,1)
Sistem
{-1<(1-y)/(1+y)=>-1-y<1-y =>-1>1 evident
{(1-y)/(1+y)<1=> 1-y<1+y => -y<y evident pt ca y>0
Asadar ecuatia x=(1-x)/(1+y) admite solutii.functia e surjectiva
Intrebari?
