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If f(x) = x^x,then f(f(x)) =

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If f(x) = x^x,then f(f(x)) = [#permalink]

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If \(f(x)= x^x,\) then \(f(f(x))=\)

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[Reveal] Spoiler:
Got this Question in Veritas prep test . Can this question be done by plugging in some values..
[Reveal] Spoiler: OA

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If f(x) = x^x,then f(f(x)) = [#permalink]

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\(f(x) = x^x\)

\(f[f(x)] = f(x)^{f(x)}\)

\(= (x^x)^{(x^x)}\)

\(= x^{(x*x^x)}\)

\(= x^{x^{1+x}}\)

= Answer = D
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Re: If f(x) = x^x,then f(f(x)) = [#permalink]

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PareshGmat wrote:
\(f(x) = x^x\)

\(f[f(x)] = f(x)^{f(x)}\)

\(= (x^x)^{(x^x)}\)

\(= x^{(x. x^x)}\)

\(= x^{x^{1+x}}\)

= Answer = D


Thanks for your reply

Would you try this question by plugging in. The question looked good for plugging in options but I am not getting the answer.
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If f(x) = x^x,then f(f(x)) = [#permalink]

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WoundedTiger wrote:
PareshGmat wrote:
\(f(x) = x^x\)

\(f[f(x)] = f(x)^{f(x)}\)

\(= (x^x)^{(x^x)}\)

\(= x^{(x. x^x)}\)

\(= x^{x^{1+x}}\)

= Answer = D


Thanks for your reply

Would you try this question by plugging in. The question looked good for plugging in options but I am not getting the answer.


From the derived answer:

\(f(3) = 3^{3^{(1+3)}}\)

\(= 3^{(3^4)}\)

\(= 3^{81}\)........... (1)

\(f[f(3)] = (3^3)^{(3^3)}\)

\(= (3^3)^{27}\)

\(= 3^{(27*3)}\)

\(= 3^{81}\) ............ (2)

(1) = (2)
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Last edited by PareshGmat on 25 Sep 2014, 17:40, edited 1 time in total.

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If f(x) = x^x,then f(f(x)) = [#permalink]

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Please note:

\(2^{3^2} = 2^{(3^2)} = 2^9 = 512\)

\((2^3)^2 = 2^{(3*2)} = 2^6 = 64\)

OR

\((2^3)^2 = 8^2 = 64\)

Power calculations go from top to bottom, if brackets are not provided
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Re: If f(x) = x^x,then f(f(x)) = [#permalink]

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New post 23 Jun 2014, 04:49
WoundedTiger wrote:
If \(f(x)= x^x,\) then \(f(f(x))=\)

Attachment:
Untitled.png



[Reveal] Spoiler:
Got this Question in Veritas prep test . Can this question be done by plugging in some values..


Added this question to functions directory in Special Questions Directory

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
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Re: If f(x) = x^x,then f(f(x)) = [#permalink]

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New post 07 Oct 2017, 07:07
Bunuel wrote:
WoundedTiger wrote:
If \(f(x)= x^x,\) then \(f(f(x))=\)

Attachment:
Untitled.png



[Reveal] Spoiler:
Got this Question in Veritas prep test . Can this question be done by plugging in some values..


Added this question to functions directory in Special Questions Directory

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions


hi Bunuel

the use of exponents is little bit trickier to me here

please let me understand...

f [ f(x) ] to the power f(x)
that is [ f (x) ] is raised to power f(x)..

NOT, f (x) is raised to power f(x), if this is so, then it may mean, in f(x), "x" is raised to the power f(x), and thus may end up with result looking like option A

So, the expression here is meant to be "[ f (x) ]" (the whole) is raised to the power f(x)" and thus option D is right
Am I right or wrong ....? please help me get rid of my doubts ...

thanks in advance, man

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Re: If f(x) = x^x,then f(f(x)) = [#permalink]

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New post 07 Oct 2017, 07:20
gmatcracker2017 wrote:
Bunuel wrote:
WoundedTiger wrote:
If \(f(x)= x^x,\) then \(f(f(x))=\)

Attachment:
Untitled.png



[Reveal] Spoiler:
Got this Question in Veritas prep test . Can this question be done by plugging in some values..


Added this question to functions directory in Special Questions Directory

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions


hi Bunuel

the use of exponents is little bit trickier to me here

please let me understand...

f [ f(x) ] to the power f(x)
that is [ f (x) ] is raised to power f(x)..

NOT, f (x) is raised to power f(x), if this is so, then it may mean, in f(x), "x" is raised to the power f(x), and thus may end up with result looking like option A

So, the expression here is meant to be "[ f (x) ]" (the whole) is raised to the power f(x)" and thus option D is right
Am I right or wrong ....? please help me get rid of my doubts ...

thanks in advance, man


Paresh HERE explains it so perfectly that I have nothing to add.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135613 [0], given: 12705

Re: If f(x) = x^x,then f(f(x)) =   [#permalink] 07 Oct 2017, 07:20
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