Well,
X=X^2
Only 1 and 0 will satisfy this
So how about E
Function problem
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Ian Stewart
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The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):logitech wrote:Well,
X=X^2
Only 1 and 0 will satisfy this
So how about E
Since f(x) = f(x^2), f(-2) must be equal to f((-2)^2) = f(4). Further, f(4) must be equal to f(16). So f(-2) = f(16), and B) must be true.
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logitech
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Thanks Ian.Ian Stewart wrote:The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):logitech wrote:Well,
X=X^2
Only 1 and 0 will satisfy this
So how about E
Since f(x) = f(x^2), f(-2) must be equal to f((-2)^2) = f(4). Further, f(4) must be equal to f(16). So f(-2) = f(16), and B) must be true.
f(-2) = f(16) in this case. B it is
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
I don't understand how your saying that F(-2)= f(16)??? f(-2) is F(-2^2) = 4Ian Stewart wrote:The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):logitech wrote:Well,
X=X^2
Only 1 and 0 will satisfy this
So how about E
Since f(x) = f(x^2), f(-2) must be equal to f((-2)^2) = f(4). Further, f(4) must be equal to f(16). So f(-2) = f(16), and B) must be true.
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logitech
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anf F(4) = F(4^2) and it goes and goes...ajmoney09 wrote:I don't understand how your saying that F(-2)= f(16)??? f(-2) is F(-2^2) = 4Ian Stewart wrote:The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):logitech wrote:Well,
X=X^2
Only 1 and 0 will satisfy this
So how about E
Since f(x) = f(x^2), f(-2) must be equal to f((-2)^2) = f(4). Further, f(4) must be equal to f(16). So f(-2) = f(16), and B) must be true.
this function is probably something like F(x) = 2
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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Yes, f(-2) is equal to f((-2)^2), but f((-2)^2) is *not* equal to 4. It's equal to f(4). Nowhere in the question are we told what this function actually does. It might be the case that f(x) = 1000 for all values of x, for example, in which case it will certainly be true that f(x) = f(x^2) for all x, because f(anything) = f(anything else) if f(x) is always 1000.ajmoney09 wrote:I don't understand how your saying that F(-2)= f(16)??? f(-2) is F(-2^2) = 4Ian Stewart wrote:The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):logitech wrote:Well,
X=X^2
Only 1 and 0 will satisfy this
So how about E
Since f(x) = f(x^2), f(-2) must be equal to f((-2)^2) = f(4). Further, f(4) must be equal to f(16). So f(-2) = f(16), and B) must be true.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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cramya
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Yes, f(-2) is equal to f((-2)^2), but f((-2)^2) is *not* equal to 4. It's equal to f(4). Nowhere in the question are we told what this function actually does. It might be the case that f(x) = 1000 for all values of x, for example, in which case it will certainly be true that f(x) = f(x^2) for all x, because f(anything) = f(anything else) if f(x) is always 1000
Thats awesome; thanks Ian!!!!
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Ian Stewart
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You certainly can say that f(16) = f(256), but it's just not useful to do here. What we do know here is that f(x) is always equal to f(x^2). So, for example,4meonly wrote:I still do not understand why we should not make 16^2 from f(16). Why we make two second powers of -2 but do not do it with 16?
Please, help to understand! Thank you!
f(2) = f(4) = f(16) = f(256) = f(65536) = ...
and
f(3) = f(9) = f(81) = f(6561) = ...
So any of the following would be equal to zero:
f(4) - f(2)
f(256) - f(2)
f(4) - f(65536)
f(81) - f(6561)
etc
We replaced f(-2) with f(4), and then with f(16), above in order to show that f(-2) and f(16) were equal, and once we'd done that, we stopped working - the job was done. Still, we certainly could have replaced f(16) with f(256), for example; it just wasn't necessary or helpful to do so.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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