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Function Finding From Floor (Posted on 2016-09-30) Difficulty: 3 of 5
Find all functions f:R -> R such that:
f(floor(x)*y) = f(x)*floor(f(y)) holds for all x and y.

Prove that no other function satisfies the above relationship.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Some Thoughts Solution (spoiler) | Comment 1 of 2
Let y = 0.
Then f(0) = f(x)*floor(f(0))
This means that f(x) must be a constant.  Call it c.

Then, for all x and y,
c = c*floor(c)

Either c = 0 or floor(c) = 1.

So c can be 0 or c can be in [1,2)  (i,e, >=1 and <2)

  Posted by Steve Herman on 2016-10-01 12:45:56
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