Track / Stage 4 / 78 of 340 #338 of 2000

Problem 338

AMC 12 late, AIME early

Algebra Difficulty 4.7 Find the answer

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) $y=f^{-1}(-x-1)+1$

Your answer

Official solution

(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
$y=t-2=f^{-1}(-x)-2 .$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.