Let `f(x)=x^(2), x in R. " for any " A subseteq R,` define `g(A)={x in R: f(x) in A}`. If ` S=[0,4],` then which one of the following statements is not ture?(A) `f(g(S))=S`(B) `g(f(S)) ne S`(C) `g(f(S)) =g(S)`(D) `f(g(S))ne f(S)`A. `f(g(S))=S`B. `g(f(S)) ne S`C. `g(f(S)) =g(S)`D. `f(g(S))ne f(S)`

Let `f(x)=x^(2), x in R. " for any " A subseteq R,` define `g(A)={x in

1.	Let `f(x)=x^(2), x in R. " for any " A subseteq R,` define `g(A)={x in R: f(x) in A}`. If ` S=[0,4],` then which one of the following statements is not ture?(A) `f(g(S))=S`(B) `g(f(S)) ne S`(C) `g(f(S)) =g(S)`(D) `f(g(S))ne f(S)`A. `f(g(S))=S`B. `g(f(S)) ne S`C. `g(f(S)) =g(S)`D. `f(g(S))ne f(S)`
Answer» Correct Answer - C Given, Function `f(x)=x^(2), x in R` ` and g(A)={x in R: f(x) in A}: A subseteq R` Now, for `S=[0,4]` `g(S)={x in R: f(x) in S=[0,4]}` `={x in R: x^(2) in [0,4]}` `={x in R: x in [-2,2]}` `rArr g(S)=[-2,2]` So, `f(g(S))=[0,4]=S` Now, `f(S)={x^(2): x in S =[0,14]} =[0,16]` `and g(f(S))={x in R: f(x) in f(S)=[0,16]}` `={x in R: f(x) in [0,16]}` `={x in R: x^(2) in [0,16]}` `={ x in R: x in [-4,4]}=[-4,4]` From above, it is clear that `g(f(S))=g(S).`