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# If f(x)=x^2 and x is a positive integer, which of the following CANNOT

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If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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28 Feb 2016, 09:37
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If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?

A. 1
B. 16
C. 81
D. 144
E. 256
[Reveal] Spoiler: OA

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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28 Feb 2016, 21:21
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Bunuel wrote:
If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?

A. 1
B. 16
C. 81
D. 144
E. 256

f(x)=x^2
f(f(x)) = (x^2)^2
=x^4

A. 1 , x=1
B. 16 , x=2
C. 81 , x=3
D. 144
f(x)=12
Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) .
E. 256 , x=4

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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03 Mar 2016, 03:18
Bunuel wrote:
If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?

A. 1
B. 16
C. 81
D. 144
E. 256

f(x)=x^2
f(f(x)) = (x^2)^2 = x^4
Therefore f(f(x)) will be numbers that are 4th power of other numbers.

Checking the options:

A. 1 = 1^\$
B. 16 = 2^4
C. 81 = 3^4
D. 144. This cannot be written as the 4th power of any number
E. 256 = 4^4

Correct Option: D
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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03 Mar 2016, 17:23
If you memorized the first ten powers of two as well as the first five powers of three, then this question takes you less than thirty seconds.

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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02 Jul 2017, 12:17
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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05 Aug 2017, 05:44
hello! So i got it till here:
f(x)= x square so f(f(x)) = F(x square) = x^4
now, 16,81,256 are all fourth of 2^2, 3^4 and 4^4 -- how is it that 4^ 4 is the answer?
Would appreciate some detail on the explanation, thank you!

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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05 Aug 2017, 06:18
Bunuel wrote:
If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?

A. 1
B. 16
C. 81
D. 144
E. 256

f(x) = x^2
f(f(x)) = (x^2)^2 = x^4

A. 1^4
B. 2^4
C. 3^4
D. 12^2
E. 4^4

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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05 Aug 2017, 06:32
shashankism wrote:
Bunuel wrote:
If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?

A. 1
B. 16
C. 81
D. 144
E. 256

f(x) = x^2
f(f(x)) = (x^2)^2 = x^4

A. 1^4
B. 2^4
C. 3^4
D. 12^2
E. 4^4

Hi wanted to re-iterate my query. I asked why is 4^4 the right answer, since 2,3 and 1 are all raised to power 4 in the options. So I am not able to understand why only 4^4 is the answer and not 1,2 or 3. Thank you

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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05 Aug 2017, 06:50
shashankism wrote:
Bunuel wrote:
If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?

A. 1
B. 16
C. 81
D. 144
E. 256

f(x) = x^2
f(f(x)) = (x^2)^2 = x^4

A. 1^4
B. 2^4
C. 3^4
D. 12^2
E. 4^4

Hi wanted to re-iterate my query. I asked why is 4^4 the right answer, since 2,3 and 1 are all raised to power 4 in the options. So I am not able to understand why only 4^4 is the answer and not 1,2 or 3. Thank you

Madhavi1990 12^2 is the answer and not 4^4 .. I have mentioned option D i.e. 12^2. Please look carefully into my solution .
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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05 Aug 2017, 07:21
I did actually, but didnt understand why 144 is the answer if its 12^2 (f(x) = x^2
f(f(x)) = (x^2)^2 = x^4. Isn't it supposed to be a power of 4? How does 12 feature as a power of 4? Please do clarify

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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05 Aug 2017, 08:52
I did actually, but didnt understand why 144 is the answer if its 12^2 (f(x) = x^2
f(f(x)) = (x^2)^2 = x^4. Isn't it supposed to be a power of 4? How does 12 feature as a power of 4? Please do clarify

It says CANNOT be the value of f(f(x)).

Only 144 is not the fourth power of any integer. Hope this helps.

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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05 Aug 2017, 09:10
Bunuel wrote:
If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?

A. 1
B. 16
C. 81
D. 144
E. 256

x = 1
f(f(x)) = $$x^4$$ = $$1^4$$ = 1.

x = 2
f(f(x)) = $$x^4$$ = $$2^4$$ = 16.

x = 3
f(f(x)) = $$x^4$$ = $$3^4$$ = 81.

x = 4
f(f(x)) = $$x^4$$ = $$4^4$$ = 256.

Above are all values of f(f(x)) for all x = positive integer.

144 = $$12^2$$ => It cannot be written in the form $$x^4$$ as no integer to the power of 4 results in 144.
And that is why D is the answer.
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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05 Aug 2017, 14:08
I did actually, but didnt understand why 144 is the answer if its 12^2 (f(x) = x^2
f(f(x)) = (x^2)^2 = x^4. Isn't it supposed to be a power of 4? How does 12 feature as a power of 4? Please do clarify

The question is asking which option is not of the type x^4
Clearly 12^2 is not of the type x^4 .. Hope that helps..
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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT [#permalink]

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06 Aug 2017, 06:54
akshayk wrote:
Bunuel wrote:
If f(x)=x^2 and x is a positive integer, which of the following CANNOT be the value of f(f(x))?

A. 1
B. 16
C. 81
D. 144
E. 256

x = 1
f(f(x)) = $$x^4$$ = $$1^4$$ = 1.

x = 2
f(f(x)) = $$x^4$$ = $$2^4$$ = 16.

x = 3
f(f(x)) = $$x^4$$ = $$3^4$$ = 81.

x = 4
f(f(x)) = $$x^4$$ = $$4^4$$ = 256.

Above are all values of f(f(x)) for all x = positive integer.

144 = $$12^2$$ => It cannot be written in the form $$x^4$$ as no integer to the power of 4 results in 144.
And that is why D is the answer.

Thank you,this was insightful

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Re: If f(x)=x^2 and x is a positive integer, which of the following CANNOT   [#permalink] 06 Aug 2017, 06:54
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