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by logitech » Wed Jan 14, 2009 10:28 am
Well,

X=X^2

Only 1 and 0 will satisfy this

So how about E
LGTCH
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by Ian Stewart » Wed Jan 14, 2009 12:21 pm
logitech wrote:Well,

X=X^2

Only 1 and 0 will satisfy this

So how about E
The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):

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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by logitech » Wed Jan 14, 2009 12:24 pm
Ian Stewart wrote:
logitech wrote:Well,

X=X^2

Only 1 and 0 will satisfy this

So how about E
The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):

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.
Thanks Ian.

f(-2) = f(16) in this case. B it is
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by ajmoney09 » Wed Jan 14, 2009 12:26 pm
Ian Stewart wrote:
logitech wrote:Well,

X=X^2

Only 1 and 0 will satisfy this

So how about E
The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):

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.
I don't understand how your saying that F(-2)= f(16)??? f(-2) is F(-2^2) = 4
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by logitech » Wed Jan 14, 2009 12:29 pm
ajmoney09 wrote:
Ian Stewart wrote:
logitech wrote:Well,

X=X^2

Only 1 and 0 will satisfy this

So how about E
The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):

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.
I don't understand how your saying that F(-2)= f(16)??? f(-2) is F(-2^2) = 4
anf F(4) = F(4^2) and it goes and goes...

this function is probably something like F(x) = 2
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by Ian Stewart » Wed Jan 14, 2009 5:30 pm
ajmoney09 wrote:
Ian Stewart wrote:
logitech wrote:Well,

X=X^2

Only 1 and 0 will satisfy this

So how about E
The question doesn't say that x = x^2; it says that f(x) = f(x^2). The answer should be B):

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.
I don't understand how your saying that F(-2)= f(16)??? f(-2) is F(-2^2) = 4
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.
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by cramya » Wed Jan 14, 2009 5:42 pm
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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by 4meonly » Wed Jan 14, 2009 11:33 pm
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!
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by Ian Stewart » Thu Jan 15, 2009 1:01 am
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!
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,

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.
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