x = log left( frac{1}{y} + sqrt{1 + frac{1}{y | vedclass

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(D) Given, $x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right)$.We know that the inverse hyperbolic cosecant function is defined as $\oper

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$\operatorname{cosech} x$

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(D) Given, $x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right)$.We know that the inverse hyperbolic cosecant function is defined as $\operatorname{cosech}^{-1} y = \log \left( \frac{1}{y} + \sqrt{\frac{1}{y^2} + 1} \right)$.Comparing this with the given equation, we get $x = \operatorname{cosech}^{-1} y$.Taking the hyperbolic cosecant on both sides, we get $y = \operatorname{cosech} x$.

$x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right) \Rightarrow y$ is equal to

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