Answer
$\begin{align*}
(a)& \quad 1.317 \\
(b)& \quad 0.962 \end{align*}$
Work Step by Step
Use Th. 5.19
$\cosh^{-1}x=\ln(x+\sqrt{x^{2}-1})\qquad $Domain: $[1, \infty)$
$\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{h}^{-1} x=\displaystyle \ln\frac{1+\sqrt{1-x^{2}}}{x}\qquad $Domain: $(0,1]$
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(a)
$\cosh^{-1}2=\ln(2+\sqrt{3})\approx 1.317$
(b)
$\displaystyle \mathrm{s}\mathrm{e}\mathrm{c}\mathrm{h}^{-1}\frac{2}{3}=\ln(\frac{1+\sqrt{1-(\frac{2}{3})^{2}}}{\frac{2}{3}})\approx 0.962$
