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Question:
Let $\mathrm{f}(\mathrm{x})=\log _{\mathrm{e}}(\sin \mathrm{x}),(0<\mathrm{x}<\pi)$ and $g(x)=\sin ^{-1}\left(e^{-x}\right),(x \geq 0)$. If $\alpha$ is a positive real number such that $\mathrm{a}=(\mathrm{fog})^{\prime}(\alpha)$ and $\mathrm{b}=(\mathrm{fog})(\alpha)$, then :
Correct Option: , 4
Solution:
fog $(x)=(-x) \Rightarrow(f g(\alpha))=-\alpha=b$
$(f g(x))^{\prime}=-1 \Rightarrow(f g(\alpha))^{\prime}=-1=a$
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