Back on topic, I tried it and got f(f(x)) = a (ax + b|x|) + b|(ax + b|x|)|.
For g(g(x)) to equal x when f(f(x)) is equal to x, then f(f(x) would have to be equal to g(g(x) and so b would have to be 0.
So now you have to prove that a (ax + b|x|) + b|(ax + b|x|)| ≠ x for all values of x when b ≠ 0. That's the tricky bit.
]]>f(x) = ax + b|x| and g(x) = ax - b|x|
Show that if: f(f(x)) = x for every real x, then:
g(g(x)) = x for every real x
Pleas help 'cause I haven't got any idea how to solve it.
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