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Let f(x) = x 2 , x ∈ R. For any A ⊆ R, define g (A) = { x ∈ R : f(x) ∈ A}. If S = [0,4], then which one of the following statements is not true ?

1. g(f(S)) ≠ S
2. f(g(S)) = S
3. f(g(S)) ≠ f(S)
4. g(f(S)) = g(S)

Correct answer: g(f(S)) = g(S)

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