It seems like the problem statement is incomplete. However, I will help you understand how to find the domain of a function, which may help you decide how to complete your problem.
To find the domain of a function, we typically look for values of \(x\) for which the function is defined. Here are some general guidelines:
1. **For Polynomial Functions:**
Polynomial functions are defined for all real numbers. So, their domain is all real numbers, \((-\infty, \infty)\).
2. **For Rational Functions:**
A rational function has the form \(\frac{P(x)}{Q(x)}\), where \(P(x)\) and \(Q(x)\) are polynomials. The domain consists of all real numbers except those that make the denominator \(Q(x)\) equal to \(0\).
3. **For Radical Functions:**
For a function involving a square root, like \(\sqrt{f(x)}\), the domain consists of all real numbers for which \(f(x) \geq 0\). This applies only to even roots (square roots, fourth roots, etc.).
4. **For Logarithmic Functions:**
A logarithmic function \(\log(f(x))\) is defined only for positive arguments. So, the domain consists of all \(x\) for which \(f(x) > 0\).
Given the choices:
- \(x > 6\)
- \(x \ge 6\)
- \(x \ge -6\)
- Something to do with the domain
Let’s assume your function looks something like this:
**Example 1 (Radical Function):**
\[ f(x) = \sqrt{x - 6} \]
To find the domain:
\[ x - 6 \ge 0 \]
\[ x \ge 6 \]
So the domain is \( x \ge 6 \), which corresponds to the fourth choice.
**Example 2 (Rational Function):**
\[ f(x) = \frac{1}{x + 6} \]
To find the domain:
\[ x + 6 \ne 0 \]
\[ x \ne -6 \]
So the domain is all real numbers except \( -6 \), which does not match any of the given choices exactly.
However, since we are considering a likely radical function as aligned with the given options, the most relevant answer to a domain definition problem for a square root function is:
\[ \text{Domain: } x \ge 6 \]
So based on standard domain-finding techniques, the fourth option (\(x \ge 6\)) is the most logically consistent within a typical context provided by such questions.
8.
Find the domain of .
x ≥
x > 6
x ≥ −6
x ≥ 6
1 answer