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

Question:

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

1. $g(f(S)) \neq S$

2. $f(g(S))=S$

3. $g(f(S))=g(S)$

4. $f(g(S)) \neq f(S)$

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year April 10, 2019 (I)

Solution:

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