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Question

Let  f(x)=x2,xR. For any AR, define g(A)={xR:f(x)A}. If S=[0,4], then which one of the following statements is not true ?


A
f(g(S))f(S)
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B
f(g(S))=S
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C
g(f(S))S
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D
g(f(S))=g(S)
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Solution

The correct option is D g(f(S))=g(S)
f(S)=S2f(S)[0,16]
g(S)={x:xR,x2S}
g(S)[2,2]
g(f(S))={x:f(x)f(S)}             ={x:x2[0,16]}
g(f(S))[4,4]

f(g(S))=(g(S))2f(g(S)[0,4]


Mathematics

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