Compute the infimum and supremum of $A=\{f(x)=\frac{2x+1}{x+2}: x>-2\}$.  

I try to do these following passages:
since $f$ is derivable I compute $f'(x)=\frac{3}{x+2}>0$ and so from Monotone Convergence Theorem I can conclude that:
$\lim\_{x\to-2^+}f(x)=-\infty=infA$ and $\lim\_{x\to+\infty}f(x)=2=supA$. All right?