Question

Define a function f(x) such that f(f(x)) = -x

Answer 1

\[f(x)=-|x|\]

Answer 2

\[f(f(x)) = -|-|x||\]\[f(f(-1)) \neq 1 \]

Answer 3

@Anwar

f(f(x)) = -(-x) = x :-P

Answer 4

:/

Answer 5

This can be done in a few lines in Python.

Python 1, Math 0 :-D

Answer 6

why not C?

Answer 7

It might be possible in C..... let me think

Answer 8

maybe easier in C++

Answer 9

because Python (at least the default one) is C's baby, and if Python can do it, then C can :-D

Answer 10

in python you can't even i++ :D

Answer 11

What's the definition of the function? Don't give us Python code; the code is just the encapsulation of that definition. What is the definition itself in ordinary mathematical notation?

Answer 12

I was hoping someone could figure it out for me :( I think it has to do with complex numbers.

f(x) = x*i

Answer 13

oh, so it's not a real valued function? Then it's trivial.

Answer 14

right

Answer 15

but the question said we can't use complex numbers :(

Answer 16

In which case, it's not trivial. Do you know the answer? I don't. I'd like you to tell me.

Answer 17

I don't know either, but it's one line in Python

Answer 18

f = lambda x: (lambda: -x) if (not hasattr(x, '__call__')) else x()

Answer 19

decode the line for us and tell us then. You're the Python expert.

Answer 20

I can't read that.

Answer 21

it just says f is a function that returns a function that returns the additive inverse of a number if the argument is not a function and calls its input otherwise.

Answer 22

Oh, so it's not a regular mathematical function at all.

Answer 23

is it possible to make it a regular math function?

Answer 24

i don't think so, but i'll think about it a little.