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Home/ Questions/Q 167891
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Asked: May 11, 20262026-05-11T12:21:21+00:00 2026-05-11T12:21:21+00:00

Design a function f such that: f(f(x)) == 1/x Where x is a 32

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Design a function f such that:

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

Where x is a 32 bit float

Or how about

Given a function f, find a function g such that

f(x) == g(g(x))


See Also

Interview question: f(f(n)) == -n

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  1. 2026-05-11T12:21:22+00:00Added an answer on May 11, 2026 at 12:21 pm

    For the first part: this one is more trivial than f(f(x)) = -x, IMO:

    float f(float x) {     return x >= 0 ? -1.0/x : -x; } 

    The second part is an interesting question and an obvious generalization of the original question that this question was based on. There are two basic approaches:

    • a numerical method, such that x ≠ f(x) ≠ f(f(x)), which I believe was more in the spirit of the original question, but I don’t think is possible in the general case
    • a method that involves g(g(x)) invoking f exactly once
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