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17 May 2024, 12:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
91% (00:24) correct
8% (00:07) wrong based on 12 sessions
History
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The figure above shows the graph of the function f in the xy-plane. What is the value of f (f (-1))?
A. -2
B. -1
C. 0
D. 1
E. 2
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GMAT-Club-Forum-q6bdsgfm.jpeg [ 28.84 KiB | Viewed 243 times ]
19 May 2024, 13:23
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When we look at the given graph we see that the point (-1, 2) lies ON the graph.
So, we can say "when x = -1, y = 2"
This is exactly the same as saying f(-1) = 2
Now that f(f(-1)) = f(2), what is the value of f(2)?
This is the same as asking "What's the value of y when x = 2?"
When we look at the given graph we see that the point (2, 1) lies ON the graph.
So, we can say "when x = 2, y = 1"
In other words, f(2) = 1
So, f(f(-1)) = f(2) = 1
Answer: D
So, we can say "when x = -1, y = 2"
This is exactly the same as saying f(-1) = 2
Now that f(f(-1)) = f(2), what is the value of f(2)?
This is the same as asking "What's the value of y when x = 2?"
When we look at the given graph we see that the point (2, 1) lies ON the graph.
So, we can say "when x = 2, y = 1"
In other words, f(2) = 1
So, f(f(-1)) = f(2) = 1
Answer: D
22 Jun 2024, 03:19
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Official Explanation
Note that to find f (f (-1)), you must apply the function f twice, first to find the value of f (-1) and then to find the value of f (f (-1)). To find the value of f (-1), 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 (-1)) = 1.
The correct answer is Choice D.
Note that to find f (f (-1)), you must apply the function f twice, first to find the value of f (-1) and then to find the value of f (f (-1)). To find the value of f (-1), 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 (-1)) = 1.
The correct answer is Choice D.
