Relations & Functions
Domain of a Function
Grade 12

Question:

<p>The function \( f(x) = \sqrt{x-5} \) is defined for \( x \geq 5 \). What is the domain of \( f \)?</p>
<p>\([5, \infty)\)</p>
<p>\((5, \infty)\)</p>
<p>\((-\infty, 5]\)</p>
<p>\(\mathbb{R}\)</p>

Step-by-Step Solution

Key Concept: The domain of a function is the set of all x-values for which the function is defined. For square root functions, the expression under the radical must be non-negative.
<p><strong>Step 1:</strong> Identify the constraint for the square root function. For √(x-5) to be defined in real numbers, we need x - 5 ≥ 0.</p><p><strong>Step 2:</strong> Solve the inequality: x - 5 ≥ 0 ⟹ x ≥ 5.</p><p><strong>Step 3:</strong> Express the domain in interval notation: [5, ∞) or in set notation: {x ∈ ℝ | x ≥ 5}.</p><p>∴ Answer: A</p>
Correct Answer: A

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