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…
Mathematics · JEE Main · NTA Exams — Sets, Relations and Functions
Let \(f(x)=x^{2}, x \in R\). 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?
- g(f(S)) ≠ S
- f(g(s)) = S
- f(g(S)) ≠ f(S)
- g(f(S)) = g(S)
Answer
(D) g(f(S)) = g(S)
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