JEE Main 2019 · 10 Apr · Shift I

JEE Main 2019 Mathematics question on Sets Relations and Functions

Let f(x)=x2,x∈Rf(x) = x^2, x \in R. For any A⊆RA \subseteq R, define g(A)={x∈R:f(x)∈A}g(A) = \{x \in R : f(x) \in A\}. If S=[0,4]S = [0, 4], then which one of the following statements is not true?
  1. A.
    f(g(S))=Sf(g(S)) = S
  2. B.
    g(f(S))≠Sg(f(S)) \neq S
  3. C.
    g(f(S))=g(S)g(f(S)) = g(S)
  4. D.
    f(g(S))≠f(S)f(g(S)) \neq f(S)
Show answer

Correct option: C

[JEE Main 2019 · 10 Apr · Shift I]

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