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Question

Let f(x) = sin x and g(x) = ln|x|. If the ranges of the composite functions fog and gof are R1 and R2 respectively, then

A
R1={u:1<u<1},R2={v:<v<0}
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B
R1={u:<u0},R2{v:1v1}
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C
R1={u:1<u<1},R2={v:>v<0}
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D
R1={u:1u1},R2={v:<v0}
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Solution

The correct option is D R1={u:1u1},R2={v:<v0}
fog=f(g(x))=sin ln|x|and gof=g(f(x))=ln|sinx|
R1=[1,1]andR2=(,0].)(|sinx|ϵ[0,1])

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