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If $\mathrm{g}(\mathrm{x})=\sin \mathrm{x}, \mathrm{x} \in \mathrm{R}$ and $\mathrm{f}(\mathrm{x})=\frac{1}{\sin \mathrm{x}}, \mathrm{x} \in\left(0, \frac{\pi}{2}\right)$ what is (gof) (x) equal to?
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Verified Answer
The correct answer is:
$\sin \left(\frac{1}{\sin \mathrm{x}}\right)$
Given function are :
$g(x)=\sin x$ and $f(x)=\frac{1}{\sin x}$
$($ gof $)(x)=g[f(x)]$
$=\sin \mathrm{f}(\mathrm{x})$
$=\sin \left(\frac{1}{\sin \mathrm{x}}\right)$
$g(x)=\sin x$ and $f(x)=\frac{1}{\sin x}$
$($ gof $)(x)=g[f(x)]$
$=\sin \mathrm{f}(\mathrm{x})$
$=\sin \left(\frac{1}{\sin \mathrm{x}}\right)$
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