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Algebra Difficulty 4.8 AIME Find the answer

4. The graph of the inverse function of y=a−xx−a−1y=\frac{a-x}{x-a-1} is symmetric about the point (−1,4)(-1,4). Then the real number aa equals:

Pick one

Solution

4. B. Given y=a−xx−a−1=−1−1x−(a+1)y=\frac{a-x}{x-a-1}=-1-\frac{1}{x-(a+1)}, the center of symmetry is ((a+1),−1)((a+1),-1). The center of symmetry of its inverse function is (−1,(a+1))⇒a+1=4⇒a=3(-1,(a+1)) \Rightarrow a+1=4 \Rightarrow a=3.

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