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| A Funny Function (Posted on 2013-08-01) |
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Suppose f is a continuous function such that f(1000)=999 and f(x) · f(f(x)) = 1 for all real x. What is f(891)?
A Funny Fallacious Function?
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 | Comment 4 of 7 | 
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Call me old-fashioned, but surely ...
Specifying the domain of a function is an essential part of its definition.
There may be cases when the domain is taken for granted but, luckily,
in this case it is quite clearly stated: f(x)*f(f(x))=1 for all real x.
Our only conclusion is that f cannot be continuous.
We can reduce its domain and use it as part of a new composite
function, but making a continuous link between (999,1/999) and
(1000,999), will mean that not all the real values of x in this interval
will satisfy the equation f(x)*f(f(x))=1.
Or am I missing something?
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Posted by Harry
on 2013-08-03 11:08:40 |
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