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Q.

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

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a

R1={u:−1≤u<1},R2={v:−∞

b

R1={u:−∞

c

R1={u:−1

d

R1={u:−1≤u≤1},R2={v:−∞

answer is D.

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Detailed Solution

fx = sinx and gx=logx⇒ fogx =fgx=flogx =sinlogx ∈-1,1     since logx, range is RR1=u/ -1≤u≤1    also  , gofx =gfx=gsinx=logsinx     since 0≤sinx≤1 ⇒-∞
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