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A Funny Function (Posted on 2013-08-01) Difficulty: 3 of 5
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)?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (1 votes)

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Some Thoughts A Funny Fallacious Function? | Comment 4 of 7 |
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?

  Posted by Harry on 2013-08-03 11:08:40
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