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

Question

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

Skywalker18 · Answer

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

Answer D

TeamGMATIFY · Answer

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

mejia401 · Answer

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.

Answer D.

Madhavi1990 · Answer

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!

shashankism · Answer

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

Answer D

Madhavi1990 · Answer

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

shashankism · Answer

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 .

Madhavi1990 · Answer

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

akshayk · Answer

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

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

Sent from my iPhone using  GMAT Club Forum mobile app

akshayk · Answer

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.

shashankism · Answer

Madhavi1990 
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..

Madhavi1990 · Answer

Thank you,this was insightful

hsn81960 · Answer

Can someone pls explain me how does :
f(x) = x^2 becomes:
f(f(x)) = (x^2)^2 = x^4 ?

ConfusedSEA · Answer

D. If f(x)=x2
, then in f(f(x))
 the innermost parentheses becomes x2
, leaving f(x2)
. That means that the entire expression can be written as x4
, meaning that the correct answer must be able to be written as the fourth power of a positive integer. The only of the answer choices for which that is not the case is D. 1 is 1 to the fourth; 16 is 2 to the fourth; 81 is 3 to the fourth; and 256 is 4 to the fourth.

bumpbot · Answer

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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

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