x-1-f(x)=x-1-(x^2-x+3)/(x+1)=(x+1-x-1-x^2+x+3)/(x+1)=(-x^2+x-3)/(x+1)
x→∞ lim[(-x^2+x-3)/(x+1)]=-∞
b)f(0)=3
limf(x) x→∞ =lim(x^2-x+3)/(x+1)=∞ fiindca gradul numaratorului 2 mai mare decat gradul numitorului =1.
Deci Imf=[3,∞)=codomeniul => f surjectiva
c)asimptota
ecuatia asimptotei y=mx+n
m=limf(x)/x=lim(x^2-x+3)/(x+1)*x=1
n=lim[f(x)-mx)=lim[(x^2-x+3)/(x+1)-x]=lim(x^2-x+3-x^2-x)/(x+1)=lim-2x/(x+1)=-2
y=x-2