14. Given the line $y=k x-1$ intersects the left branch of the hyperbola $x^{2}-$ $y^{2}=1$ at points $A$ and $B$. If another line $l$ passes through point $P(-2,0)$ and the midpoint $Q$ of segment $A B$, find the range of the y-intercept $b$ of line $l$.
14. Let \( A\left(x_{1}, y_{1}\right) \) and \( B\left(x_{2}, y_{2}\right) \). From the problem, we establish the system of equations
\[
\left\{\begin{array}{l}
y=k x-1, \\
x^{2}-y^{2}=1
\end{array}\right.
\]

Eliminating \( y \) gives \(\left(1-k^{2}\right) x^{2}+2 k x-2=0\).
Given that the line intersects the left branch of the hyperbola at points \( A \) and \( B \), we have
\[
\left\{\begin{array}{l}
1-k^{2} \neq 0, \\
\Delta=(2 k)^{2}+8\left(1-k^{2}\right)>0, \\
x_{1}+x_{2}=\frac{-2 k}{1-k^{2}}<0 .
\end{array}\right.
\]

Solving this, we get \( -\sqrt{2} < k < 2+\sqrt{2} \).

Therefore, the range of \( b=\frac{2}{u} \) is
\[
(-\infty,-2) \cup(2+\sqrt{2},+\infty).
\]