Isn't f(f(x)) = -1 for all x in [0,2]? Is that what you intend inside the radical?
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f(1.9) = sign(1.9^2-2) = sign(1.61) =1, so f(f(1.9)) = f(1) = sign(1^2-2) = sign(-1) = -1.
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oh i see what you're saying.. it should be sign of the composition
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