To find a domain where the function $f(x) = (x - 7)^2$ is one-to-one and non-decreasing, we need to understand the behavior of this quadratic function.

Step 1: Analyze the function

The function $f(x) = (x - 7)^2$ is a parabola that opens upwards (since the coefficient of $x^2$ is positive). Its vertex is at $x = 7$, and the function decreases for $x < 7$ and increases for $x > 7$.

Step 2: Restrict the domain

To make the function one-to-one and non-decreasing, we need to restrict the domain to the right of the vertex, where the function is non-decreasing. This means we take the domain from $x = 7$ to $\infty$.

Step 3: Write the domain

The domain on which the function is one-to-one and non-decreasing is: $[7, \infty)$

Would you like more details, or do you have any questions?

Here are some related questions to further your understanding:

1. How do you determine if a function is one-to-one?
2. What is the range of the function $f(x) = (x - 7)^2$ on the domain $[7, \infty)$?
3. Why do parabolas have a vertex, and how does it relate to the function being one-to-one?
4. Can the function $f(x) = (x - 7)^2$ be one-to-one if we restrict the domain to ( (-\infty, 7