Find the domain of `f(x)=sqrt((log)_(0. 4)((x-1)/(x+5)))`

Explanation

To find the domain of the function \( f(x) = \sqrt{\log_{0.4}\left(\frac{x-1}{x+5}\right)} \), we need to ensure that the expression inside the square root is non-negative and that the logarithm is defined.

### Step 1: Ensure the logarithm is defined
The logarithm \( \log_{0.4}\left(\frac{x-1}{x+5}\right) \) is defined when its argument \( \frac{x-1}{x+5} \) is positive. Therefore, we need:
\[ \frac{x-1}{x+5} > 0 \]

...