To find the domain of the given function $y = \log_7 \left( (2 - x)^3 \right)$, we analyze the expression inside the logarithm. The argument of a logarithmic function must be strictly positive, so we require:

$(2 - x)^3 > 0$

Since the cube of any number maintains the sign of the base, the inequality simplifies to:

$2 - x > 0$

Rearranging this, we find:

$x < 2$

Thus, the domain of the function is:

$x \in (-\infty, 2)$

This means that $x$ must be less than $2$ for the logarithmic function to be defined.

Would you like further clarification or additional details? Here are some related questions:

1. How do logarithmic properties affect the domain of a function?
2. What happens if the base of the logarithm is changed to a different number?
3. Can $x = 2$ be included in the domain under any circumstances?
4. How would the domain change if the exponent of the argument were even instead of odd?
5. What are the steps to graph this function and verify the domain visually?

Tip: Always ensure that the argument of a logarithmic function is positive before proceeding with further analysis.