The figure above shows the graph of the function f in the xy-plane. What is the value of f(f(-1))?

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问题

The figure above shows the graph of the function f in the xy-plane. What is the value of f(f(-1))?

选项 A、-2
B、-1
C、0
D、1
E、2

答案D

解析 Note that to find f(f(-l)), you must apply the function f twice, first to find the value of f(-1)and then to find the value of f(f(-l)). To find the value of f(-l), find the point on the graph of the function f whose x-coordinate is x =-1. This point has y-coordinate y = 2. Therefore, the value of f(-1)is 2, and f(f(-1))= f(2). Next you need to find the value of f(2). To find the value of f(2), find the point on the graph whose x-coordinate is x = 2. This point has y-coordinate y = 1. Therefore, f(2)= 1, and because f(f(-1))= f(2), you can conclude that f(f(-l))= 1. The correct answer is Choice D.

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