2 Given the function $y=f(x)$ has an inverse function $y=f^{-1}(x)$, the graph of $y=f(x)$ is rotated counterclockwise by $90^{\circ}$ around $(1,-1)$, the equation of the resulting curve is ( ).
(A) $y=f^{-1}(-x)-2$
(B) $y=-f^{-1}(-x)-2$
(C) $y=f^{-1}(-x+1)-1$
(D) $y=f^{-1}(-x-1)+1$
(2) A Hint: The point $(t, f(t))$ rotates $90^{\circ}$ around $(1,-1)$, resulting in $(-f(t), t-$
2). Let $x=-f(t)$, then $t=f^{-1}(-x)$, thus
$$
y=t-2=f^{-1}(-x)-2 .
$$