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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) = 3*F(3)(E) F(0) = 0Source: GMAT Club Tests - hardest GMAT questions Between B and E, which one is correct and why?
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snkrhed wrote: the key to solving this problem is that if not given a restriction as in b... the function can go on forever right? Below is a detailed solution of this problem. Hope it helps. 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) = 0C. f(-2) + f(4) = 0D. f(3) = 3f(3)E. f(0) = 0We are told that some function f(x) has following property f(x) = f(x^2) for all values of x. Note that we don't know the actual function, just this one property of it. For example for this function f(3)=f(3^2) --> f(3)=f(9), similarly: f(9)=f(81), so f(3)=f(9)=f(81)=.... Now, the question asks: which of the following MUST be true? A. f(4)=f(2)*f(2): we know that f(2)=f(4), but it's not necessary f(2)=f(2)*f(2) to be true (it will be true if f(2)=1 or f(2)=0 but as we don't know the actual function we can not say for sure); B. f(16) - f(-2) = 0: again f(-2)=f(4) =f(16)=... so f(16)-f(-2)=f(16)-f(16)=0 and thus this option is always true; C. f(-2) + f(4) = 0: f(-2)=f(4), but it's not necessary f(4) + f(4)=2f(4)=0 to be true (it will be true only if f(4)=0, but again we don't know that for sure); D. f(3)=3*f(3): is 3*f(3)-f(3)=0? is 2*f(3)=0? is f(3)=0? As we don't know the actual function we can not say for sure; E. f(0)=0: And again as we don't know the actual function we can not say for sure. Answer: B.
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When F(x) = F(x²) for all x, then F must be a constant function. That means F(0)=F(1)=F(...) whatever. That is why B must be correct.
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balboa wrote: 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) = 3*F(3)
e) F(0) = 0 Given : F(x) = F (x^2) F(-2) = F (-2^2) = F (4) F(4) = F(4^2) = F(16) Therefore, F(16) - F(-2) = F (16) - F(16)=0 Ans is B
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You cant come to the conclusion that F(0) = 0 There is not information given about the vlaue of F(x).
Whats the OA?
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LoyalWater wrote: balboa wrote: 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) = 3*F(3)
e) F(0) = 0 Given : F(x) = F (x^2) F(-2) = F (-2^2) = F (4) F(4) = F(4^2) = F(16) Therefore, F(16) - F(-2) = F (16) - F(16)=0 Ans is B I don't understand why F(-2) is taken to the 4th power....when the original function states that is to be taken to the 2nd power.
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Refer to the second post in this thread. The trick is here: F(-2)=F(4) and also F(4)=F(16) therefore F(-2)=F(16) I hope this helps.
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It does not provide information about the value of F(x) or F(x^2) .. so we can not perform any operation with F(x) or F(x^2).
The leaves us only F(16) - F(-2) = 0 and F(-2)+F(4) = 0 to be examined..
F(x) = F(x^2) => f(-2) = f(4) =f(16) .. so B is the answer.
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hear F(x)=F(x^2) but not any specific operation so, F(x) = F(x^2) => f(-2) = f(4) =f(16) .. so B is the answer.
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F(-2) = F((-2)^2) = F(4) F(4) = F(4^2) = F(16) => F(16) - F(-2) = 0 Answer - B
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Just by going the same logic why "C" cant be the answer? As (-2)^2 = 4
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vijayahir wrote: Just by going the same logic why "C" cant be the answer?
As (-2)^2 = 4 Because F(4) + f(4) can not be equal to zero unless F(4) = 0 which we have no information about, so the answer can not be C.
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balboa 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) = 3*F(3)(E) F(0) = 0Source: GMAT Club Tests - hardest GMAT questions Between B and E, which one is correct and why? If for some reason the answer is B, why not A? We are saying F(-2) = F(4) = F(16) and therefore F(16) - F(-2) => F(16) - F(16) =0 must be true. So in the above example we are doing a simple arithmetic of 16 - 16 for F(16) - F(16). Why not do 4 = 2 * 2 for F(4) = F(2)*F(2)? Can someone please help explain?
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mniyer wrote: balboa 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) = 3*F(3)(E) F(0) = 0Source: GMAT Club Tests - hardest GMAT questions Between B and E, which one is correct and why? If for some reason the answer is B, why not A? We are saying F(-2) = F(4) = F(16) and therefore F(16) - F(-2) => F(16) - F(16) =0 must be true. So in the above example we are doing a simple arithmetic of 16 - 16 for F(16) - F(16). Why not do 4 = 2 * 2 for F(4) = F(2)*F(2)? Can someone please help explain? We don't know what the function actually returns; we just know that the function returns the same value for a number and its square. e.g.. f(2^{1/4})=100 f(2^{1/2})=100 f(2)=100 f(4)=100 f(16)=100 OR f(2^{1/4})=2 f(2^{1/2})=2 f(2)=2 f(4)=2 f(16)=2 AND f(3^{1/4})=200 f(3^{1/2})=200 f(3)=200 f(9)=200 f(81)=200 Now, f(4) = f(2)*f(2) If; f(2)=0 f(4)=0 f(16)=0 f(2)*f(2)=0 f(4) = f(2)*f(2) as 0 = 0. If, f(2)=2 f(4)=2 f(16)=2 f(2)*f(2)=2*2=4 f(4) != f(2)*f(2) as 2 != 4 So, this function may be true but not MUST be true.
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What if one of the option is f(-2)-f(4)=0
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agdimple333 wrote: What if one of the option is f(-2)-f(4)=0 This will also be correct.
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balboa wrote: Do you mind telling me how E is incorrect? Because there are many possibilities other than one given what if F(x) = 1 then F(0)=1
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the key to solving this problem is that if not given a restriction as in b... the function can go on forever right?
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Bunuel wrote: snkrhed wrote: the key to solving this problem is that if not given a restriction as in b... the function can go on forever right? Below is a detailed solution of this problem. Hope it helps. 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) = 0C. f(-2) + f(4) = 0D. f(3) = 3f(3)E. f(0) = 0We are told that some function f(x) has following property f(x) = f(x^2) for all values of x. Note that we don't know the actual function, just this one property of it. For example for this function f(3)=f(3^2) --> f(3)=f(9), similarly: f(9)=f(81), so f(3)=f(9)=f(81)=.... Now, the question asks: which of the following MUST be true? A. f(4)=f(2)*f(2): we know that f(2)=f(4), but it's not necessary f(2)=f(2)*f(2) to be true (it will be true if f(2)=1 or f(2)=0 but as we don't know the actual function we can not say for sure); B. f(16) - f(-2) = 0: again f(-2)=f(4) =f(16)=... so f(16)-f(-2)=f(16)-f(16)=0 and thus this option is always true; C. f(-2) + f(4) = 0: f(-2)=f(4), but it's not necessary f(4) + f(4)=2f(4)=0 to be true (it will be true only if f(4)=0, but again we don't know that for sure); D. f(3)=3*f(3): is 3*f(3)-f(3)=0? is 2*f(3)=0? is f(3)=0? As we don't know the actual function we can not say for sure; E. f(0)=0: And again as we don't know the actual function we can not say for sure. Answer: B. Great explanation! I missed out on the initial part and got lost (f'x is the same as f'x2 the same as f'x4) - Great question! Thanks & Regards, Vishnu
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Bunuel wrote: snkrhed wrote: the key to solving this problem is that if not given a restriction as in b... the function can go on forever right? Below is a detailed solution of this problem. Hope it helps. 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) = 0C. f(-2) + f(4) = 0D. f(3) = 3f(3)E. f(0) = 0We are told that some function f(x) has following property f(x) = f(x^2) for all values of x. Note that we don't know the actual function, just this one property of it. For example for this function f(3)=f(3^2) --> f(3)=f(9), similarly: f(9)=f(81), so f(3)=f(9)=f(81)=.... Now, the question asks: which of the following MUST be true? A. f(4)=f(2)*f(2): we know that f(2)=f(4), but it's not necessary f(2)=f(2)*f(2) to be true (it will be true if f(2)=1 or f(2)=0 but as we don't know the actual function we can not say for sure); B. f(16) - f(-2) = 0: again f(-2)=f(4) =f(16)=... so f(16)-f(-2)=f(16)-f(16)=0 and thus this option is always true; C. f(-2) + f(4) = 0: f(-2)=f(4), but it's not necessary f(4) + f(4)=2f(4)=0 to be true (it will be true only if f(4)=0, but again we don't know that for sure); D. f(3)=3*f(3): is 3*f(3)-f(3)=0? is 2*f(3)=0? is f(3)=0? As we don't know the actual function we can not say for sure; E. f(0)=0: And again as we don't know the actual function we can not say for sure. Answer: B. Hi Bunuel, thanks for the explanation. I found this question to be very tough and I seem to be the only one not being able to understand this even after your explanation  I could understand why B is the answer and why not C and D. But I am still confused with A and E. I have tried to explain my thought process below - We know that f(x) = f(x^2) means f(2) = f(4) = f(16) and so on..... A. f(4)=f(2)*f(2) LHS is f(4) which means (16) RHS is f(2)*f(2) means 4*4 means (16) Hence LHS = RHS? As I am writing this, it occurred to me that here we are multiplying to functions {f(2)*f(2)} and we don't really know if multiplying of two functions will actually result in the multiplication of those two numbers/integers? it could result in some other function as well? Am I thinking in the right direction? Coming to option E - it says f(0)=0 we know that f(x) = f(x^2) if x is 0...its square (infact any exponent) or function of its square should always result in 0. I can't think through what's wrong with E? Could you please help me understand where I am going wrong. Many thanks for your help. Kind regards
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