1. The problem is to find the domain of the function $$y = \log_4 (1 - x)^7$$.\n\n2. Recall that the domain of a logarithmic function $$\log_a b$$ requires the argument $$b$$ to be strictly positive: $$b > 0$$.\n\n3. Apply this to our function: $$ (1 - x)^7 > 0 $$\n\n4. Since the exponent 7 is odd, the sign of $(1-x)^7$ is the same as the sign of $(1-x)$. Thus, $$ (1-x)^7 > 0 \iff 1-x > 0 $$\n\n5. Solve the inequality for $$x$$: $$ 1 - x > 0 \implies x < 1 $$\n\n6. Therefore, the domain of the function is all real numbers $$x$$ such that $$x < 1$$. In interval notation, this is $$(-\infty, 1)$$.\n\nFinal answer: $$\boxed{(-\infty, 1)}$$