If function f(x) satisfies f(x) = f(x^2) for all x, which of the following must be true?
(A) f(4) = f(2)f(2)
(B) f(16) - f(-2) = 0
(C) f(-2) + f(4) = 0
(D) f(3) = 3f(3)
(E) f(0) = 0
OA= B
If someone can explain the answer.
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euro
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I am not too sure but here is my explanation for choice (B)...
Given: f(x) = f(x^2)
For option (B),
f(16) = f(4^2) = f(4)
f(-2) = f(-2^2) = f(4)
Hence, f(16) - f(-2) = f(4) - f(4) = 0
Therefore, LHS = 0 = RHS.
However, I would like to know a better approach to solve this - one that is more generic.
Given: f(x) = f(x^2)
For option (B),
f(16) = f(4^2) = f(4)
f(-2) = f(-2^2) = f(4)
Hence, f(16) - f(-2) = f(4) - f(4) = 0
Therefore, LHS = 0 = RHS.
However, I would like to know a better approach to solve this - one that is more generic.
I didn't get you..euro wrote:I am not too sure but here is my explanation for choice (B)...
Given: f(x) = f(x^2)
For option (B),
f(16) = f(4^2) = f(4)
f(-2) = f(-2^2) = f(4)
Hence, f(16) - f(-2) = f(4) - f(4) = 0
Therefore, LHS = 0 = RHS.
However, I would like to know a better approach to solve this - one that is more generic.
For f(16) it has to be f(16^2) but it has been done as f(4^2), whereas for f(-2) it is done as f(-2^2)
I think it is Option (A)
f(4)=16
f(2)*f(2) = 4*4
=> 16=16
Also i have a doubt with Option (E)
As f(0)= 0^2=0
Please correct me if am wrong.
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GMATGuruNY
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The problem stipulates that f(x) = f(x^2) for all values of x.nasir wrote:If function f(x) satisfies f(x) = f(x^2) for all x, which of the following must be true?
(A) f(4) = f(2)f(2)
(B) f(16) - f(-2) = 0
(C) f(-2) + f(4) = 0
(D) f(3) = 3f(3)
(E) f(0) = 0
OA= B
If someone can explain the answer.
If x=4:
f(4) = f(4^2)
f(4) = f(16)
So f(16) = f(4).
If x= -2:
f(-2) = f((-2)^2)
So f(-2) = f(4).
Substituting into answer choice B:
f(16) - f(-2) = f(4) - f(4)
f(16) - f(-2) = 0.
Does this help?
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euro
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Thanks for the explanation Mitch. I had used the same logic but you could explain it better.GMATGuruNY wrote:
The problem stipulates that f(x) = f(x^2) for all values of x.
If x=4:
f(4) = f(4^2)
f(4) = f(16)
So f(16) = f(4).
If x= -2:
f(-2) = f((-2)^2)
So f(-2) = f(4).
Substituting into answer choice B:
f(16) - f(-2) = f(4) - f(4)
f(16) - f(-2) = 0.
Does this help?
I was wondering if theres any another way of attacking such problems (other than back solving from answer options)??
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GMATGuruNY
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I would scan the answers, looking for an answer choice that's easy to prove. I saw relatively quickly that, according to the function, f(-2) = f(4) = f(16), so it must be true that f(16) - f(-2) = 0.euro wrote:Thanks for the explanation Mitch. I had used the same logic but you could explain it better.GMATGuruNY wrote:
The problem stipulates that f(x) = f(x^2) for all values of x.
If x=4:
f(4) = f(4^2)
f(4) = f(16)
So f(16) = f(4).
If x= -2:
f(-2) = f((-2)^2)
So f(-2) = f(4).
Substituting into answer choice B:
f(16) - f(-2) = f(4) - f(4)
f(16) - f(-2) = 0.
Does this help?
I was wondering if theres any another way of attacking such problems (other than back solving from answer options)??
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Thanks a lot GuruNY..GMATGuruNY wrote:The problem stipulates that f(x) = f(x^2) for all values of x.nasir wrote:If function f(x) satisfies f(x) = f(x^2) for all x, which of the following must be true?
(A) f(4) = f(2)f(2)
(B) f(16) - f(-2) = 0
(C) f(-2) + f(4) = 0
(D) f(3) = 3f(3)
(E) f(0) = 0
OA= B
If someone can explain the answer.
If x=4:
f(4) = f(4^2)
f(4) = f(16)
So f(16) = f(4).
If x= -2:
f(-2) = f((-2)^2)
So f(-2) = f(4).
Substituting into answer choice B:
f(16) - f(-2) = f(4) - f(4)
f(16) - f(-2) = 0.
Does this help?
