Domain Analysis: Find Valid Inputs for (x-3 1/11)²

To solve this problem, we'll follow these steps:

• Step 1: Identify the expression squared in the given function.
• Step 2: Determine when the result of this squared expression is zero or greater than zero.
• Step 3: Identify any restriction on $x$ that causes $y$ not to be positive.

Now, let's work through each step:
Step 1: We have $y = \left(x - 3\frac{1}{11}\right)^2$. The expression inside the square is zero when $x = 3\frac{1}{11}$.
Step 2: Since any real number squared is non-negative, $\left(x - 3\frac{1}{11}\right)^2 \geq 0$.
Step 3: The value of $y$ is equal to zero only when $x = 3\frac{1}{11}$; for all other $x$, $y > 0$.

Therefore, the negative domain, where $y < 0$, does not exist in this function, because $y$ can never be negative.
For positive domain, the function is positive for any $x \neq 3\frac{1}{11}$, which includes all $x > 0$ except for $x = 3\frac{1}{11}$.

Conclusively, the positive and negative domains are:

x < 0 : none

x > 0 : x\ne3\frac{1}{11}