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Let f(x)=sin x and g(x)= log(e)|x|. If ...

Let `f(x)=sin x ` and `g(x)= log_(e)|x|`. If the ranges of the composition functions fog and gof are `R_(1)` and `R_(2)`, respectively, then

A

`R_(1)={u: -1 le u lt 1}, { v: -oo v lt 0}`

B

`R_(1)={u : - oo lt u lt 0}, R_(2)={v: -oo lt v lt0}`

C

`R_(1)={u: -1 lt u lt 1},R_(2)= { v: oo lt v lt 0}`

D

`R_(1)={u : -1 le u le 1}, R_(2)={v: -oo lt v lt 0}`

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The correct Answer is:
D
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