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Let f(x)=x^(2), x in R. " for any " A su...

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

`f(g(S))nef(S)`

C

`g(f(S))neS`

D

`g(f(S))=g(S)`

Text Solution

Verified by Experts

The correct Answer is:
D
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