[tex]Notam\ f(x)=y\\
\frac{-x^2-2x-3}{x^2+2x+1}=y\\
-x^2-2x-3=yx^2+2yx+y\\
x^2(-y-1)-2(y+1)x-3-y=0\\
\Delta=4(y+1)^2-4(-y-1)(-3-y)\\
\Delta=4y^2+8y-4(3y+3+y^2+y)\\
\Delta=4y^2+8y-12y+12-4y^2-4y\\
\Delta=-8y+12\\
\Delta\geq0\Rightarrow-8y+12\geq 0\\
~~~~~~~~~~~~~~12\geq 8y\\
~~~~~~~~~~~~~~y\leq \frac{3}{2}\Rightarrow y\in (-\infty,\frac{3}{2}]\\
Asadar:imf=(-\infty,\frac{3}{2}] [/tex]
