find range of 1/√(x^2-1)

Dear Student,

Please find below the solution to the asked query:
$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\sqrt{{\mathrm{x}}^2-1}} \\ \mathrm{Domain} \mathrm{of} \mathrm{this} \mathrm{function} \mathrm{will} \mathrm{be} \\ \sqrt{{\mathrm{x}}^2-1} \mathrm{is} \mathrm{not} \mathrm{equal} \mathrm{to} 0 \\ \mathrm{So} \mathrm{x} \mathrm{must} \mathrm{not} \mathrm{be} 1 \mathrm{or} -1 \\ \mathrm{And} {\mathrm{x}}^2-1>0 \\ \mathrm{So} \mathrm{the} \mathrm{domain} \mathrm{of} \mathrm{function} \mathrm{is} 1>\mathrm{x}<-1 \\ \mathrm{So} \mathrm{the} \mathrm{rangel} \mathrm{will} \mathrm{be} \\ \mathrm{f}\left(\mathrm{x}\right)>0 \mathrm{for} \mathrm{all} \mathrm{positive} \mathrm{numbers} \end{gathered}$$

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