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

Question

If f(x)= x^x, then f(f(x))= Untitled.png Got this Question in Veritas prep test . Can this question be done by plugging in some values..

PareshGmat · Accepted Answer

f(x) = x^x

f  = f(x)^{f(x)}

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

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

= x^{x^{1+x}}

= Answer = D

WoundedTiger · Answer

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.

PareshGmat · Answer

From the derived answer:

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

= 3^{(3^4)}

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

f  = (3^3)^{(3^3)}

= (3^3)^{27}

= 3^{(27*3)}

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

(1) = (2)

PareshGmat · Answer

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

Bunuel · Answer

Added this question to functions directory in  Special Questions Directory

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

testcracker · Answer

hi Bunuel

the use of exponents is little bit trickier to me here

please let me understand...

f   to the power f(x) 
that is   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 " " (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

Bunuel · Answer

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

ScottTargetTestPrep · Answer

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

Kinshook · Answer

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

IMO D

Posted from my mobile device

D4kshGargas · Answer

Even though your explanation seems plausible, but I don't think we follow such rules in our algebra classes.

Common steps of f(f(x)) 
(1) Solve f(x)
(2) Put the value of (1) in f(f(x)) thus making it f((solutionOf1))

Thus f(x) =  x^x 
and
f(f(x)) =  x^x^x^x

or let y =  x^x 
f(y) =  y^y

Thoughts?

bumpbot · Answer

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

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