The domain of definition of $\mathrm{f}\left(\mathrm{x}\right)$ $=\sqrt{{\log }_{0.4}\left(\frac{\mathrm{x}-1}{\mathrm{x}+5}\right)}\times \frac{1}{{\mathrm{x}}^2-36}\text{ is }$

For $\sqrt{{\log }_{0.4}\left(\frac{\mathrm{x}-1}{\mathrm{x}+5}\right)}$ tobe defined. We must have $0<\frac{\mathrm{x}-1}{\mathrm{x}+5}<1$ which is true if $\mathrm{x}>1$
Morever, $\frac{1}{{\mathrm{x}}^2-36}$is defined for $\mathrm{x}\ne 6,-6$ Hence the domain of$\mathrm{f}\text{ is }\{\mathrm{x}:\mathrm{x}>1,\mathrm{x}\ne 6\}$