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# Graph of the function f in the xy-plane

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Graph of the function f in the xy-plane [#permalink]  14 Dec 2015, 05:54
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Question Stats:

85% (00:40) correct 14% (00:55) wrong based on 14 sessions

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

[Reveal] Spoiler: attachment
Attachment:

Quant.jpg [ 10.9 KiB | Viewed 6391 times ]

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Question: 7
Page: 152
Difficulty: medium
[Reveal] Spoiler: OA

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GMAT Club Legend
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Re: Graph of the function f in the xy-plane [#permalink]  14 Dec 2015, 05:59
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Solution

Here we have a functions whose values are defined Graphically.

We need to compute the value of $$f(f(-1))$$. To do so we need to find the value of $$f(-1)$$ first. Now looking up the value from the graph we see that $$f(-1)= 2$$.

Hence the problem is reduced to finding the value of $$f(2)$$. Again from the graph we see that $$f(2) = 1$$.

Thus $$f(f(-1))=1$$.
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Re: Graph of the function f in the xy-plane [#permalink]  24 Jul 2017, 07:35
Could anyone explain more in detail why the solution is D. I am lost.
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Re: Graph of the function f in the xy-plane [#permalink]  25 Jul 2017, 23:57
So my understanding is - in case we have these kind of functions say f(f(f(f(-2) (say based on above graph) we keep substituting the innermost value of f? Please do let me know. thank you!
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Re: Graph of the function f in the xy-plane [#permalink]  26 Jul 2017, 06:24
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TUTTIAM52 wrote:
Could anyone explain more in detail why the solution is D. I am lost.

We evaluate the brackets first. So we find the value of $$f(-1)$$ from the graph $$f(-1)=2$$. So putting the value of $$f(-1)$$ in $$f(f(-1))=f(2)$$.

Now we look up tha value of $$f(2)$$ from the graph

nancyjose wrote:
So my understanding is - in case we have these kind of functions say f(f(f(f(-2) (say based on above graph) we keep substituting the innermost value of f? Please do let me know. thank you!

Yes you are right!
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Re: Graph of the function f in the xy-plane [#permalink]  15 Oct 2017, 19:00
Expert's post
sandy wrote:

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

[Reveal] Spoiler: attachment
Attachment:
Quant.jpg

Many people struggle with function notation.
However, it's really just the same as the "y = some expression with x" notation you've seen before (e.g., y = 3x + 1)

So, for example, asking for the value of f(-1) is the same as asking "What the value of y is when x = -1?"

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

[Reveal] Spoiler:
D

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Re: Graph of the function f in the xy-plane   [#permalink] 15 Oct 2017, 19:00
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