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Reciprocal composition is reciprocal. (Posted on 2014-02-08) Difficulty: 3 of 5
Find, if possible, two functions f and g with:

f(x) ≠ g(x)

g(x) = 1/f(x)

g(f(x)) = 1/f(g(x))

for all x in the respective domains.

No Solution Yet Submitted by Jer    
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Some Thoughts Family Plan (spoiler?) | Comment 1 of 4
Here's a whole family of satisfying functions:

g(x) = a
f(x) = 1/a

This satisfies the problem conditions if a not in {-1,0,1).  That still leaves an uncountably large number of solutions.

Given the difficulty rating of this problem, though, I suspect that Jer is looking for something a little less simple.

  Posted by Steve Herman on 2014-02-08 11:45:26
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