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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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New post 23 Jun 2014, 01:51
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If \(f(x)= x^x,\) then \(f(f(x))=\)

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Got this Question in Veritas prep test . Can this question be done by plugging in some values..

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

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New post 23 Jun 2014, 02:25
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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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New post 23 Jun 2014, 03:37
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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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New post Updated on: 25 Sep 2014, 18:40
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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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Originally posted by PareshGmat on 23 Jun 2014, 03:55.
Last edited by PareshGmat on 25 Sep 2014, 18:40, edited 1 time in total.
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If f(x) = x^x,then f(f(x)) =  [#permalink]

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New post 23 Jun 2014, 04:07
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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, 05:49
WoundedTiger wrote:
If \(f(x)= x^x,\) then \(f(f(x))=\)

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

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New post 07 Oct 2017, 08:07
Bunuel wrote:
WoundedTiger wrote:
If \(f(x)= x^x,\) then \(f(f(x))=\)

Attachment:
Untitled.png



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, 08:20
gmatcracker2017 wrote:
Bunuel wrote:
WoundedTiger wrote:
If \(f(x)= x^x,\) then \(f(f(x))=\)

Attachment:
Untitled.png



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

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New post 13 Oct 2018, 18:00
WoundedTiger wrote:
If \(f(x)= x^x,\) then \(f(f(x))=\)

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Since f(x) = x^x, f(f(x)) = f(x^x) = (x^x)^(x^x) = x^(x * x^x) = x^(x^(x + 1)).

Alternate Solution:

Let’s take x = 2. Then, f(2) = 2^2 = 4 and f(f(2)) = f(4) = 4^4 = 2^8. Let’s test each answer choice to see which one(s) simplify to 2^8:

A) x^x^x^x

If x = 2, we get 2^2^2^2 = 2^2^4 = 2^16. A is not correct.

B) x^x^x

If x = 2, we get 2^2^2 = 2^4. B is not correct.

C) x^x^x^2

If x = 2, then we get 2^2^2^2 which is the same as answer choice A. C is not correct.

D) x^x^(x + 1)

If x = 2, then we get 2^2^(2 + 1) = 2^2^3 = 2^8. D might be correct.

E) (x^x)^x

If x = 2, we get (2^2)^2 = 4^2 = 2^4. E is not correct.

Since D is the only answer choice that yields 2^8 when x is 2, D must be the correct answer choice.

Answer: D
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Re: If f(x) = x^x,then f(f(x)) =   [#permalink] 13 Oct 2018, 18:00
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