What is the domain of the function $$ y=\sqrt{x-10} $$ ? $$ \begin{array}{l}\text { A } x \geq 10 \ \text { B } x \neq 10 \ \text { C } y \geq 0\end{array} $$ D The set of all real numbers

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UpStudy AI · Accepted Answer

To determine the **domain** of the function $$ y = \sqrt{x - 10} $$, we need to identify all real numbers $$ x $$ for which the expression under the square root is **non-negative** (since the square root of a negative number is not a real number).

**Step-by-Step Reasoning:**

1. **Set the expression inside the square root to be greater than or equal to zero:**
   $$
   x - 10 \geq 0
   $$
   
2. **Solve for $$ x $$:**
   $$
   x \geq 10
   $$
   
So, the function $$ y = \sqrt{x - 10} $$ is defined for all real numbers $$ x $$ that are **greater than or equal to 10**.

**Answer Choices Analysis:**

- **A. $$ x \geq 10 $$**  
  **Correct.** This matches our solution.

- **B. $$ x \neq 10 $$**  
  **Incorrect.** $$ x = 10 $$ is included in the domain.

- **C. $$ y \geq 0 $$**  
  **Incorrect.** While this statement is true for the output $$ y $$, it does not describe the domain of $$ x $$.

- **D. The set of all real numbers**  
  **Incorrect.** The domain is restricted to $$ x \geq 10 $$.

**Final Answer:**

**A. $$ x \geq 10 $$**
The domain of the function $$ y = \sqrt{x - 10} $$ is all real numbers $$ x $$ such that $$ x \geq 10 $$.

What is the domain of the function ?

D The set of all real numbers

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What is the domain of the function ? D The set of all real numbers