<p>The domain of the function \(\sqrt{x-5}\) is \([z, \infty)\), where \(z\) is __________.</p>
Step-by-Step Solution
Key Concept: For a square root function to be defined in real numbers, the expression under the radical must be non-negative. Set the radicand ≥ 0 and solve for the minimum value of x.
<p><strong>Step 1:</strong> For √(x-5) to be defined in real numbers, the radicand must be non-negative.</p><p><strong>Step 2:</strong> Set up the inequality: x - 5 ≥ 0</p><p><strong>Step 3:</strong> Solve for x: x ≥ 5</p><p><strong>Step 4:</strong> Therefore, the domain is [5, ∞), which matches the form [z, ∞)</p><p>∴ z = <strong>5</strong></p>
Correct Answer: 5