$$ f(3)=-4 $$ Choose the correct domain. A. $$ (0,6) $$ B. $$ (-6,-2) $$ C. $$ (-\infty, \infty) $$ D. $$ (-10,10) $$ What is the set of all $$ x $$-values such that $$ f(x)=-4 ? $$ A. $$ (0,6) $$ B. $$ \{3\} $$ C. $$ \varnothing $$

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### **1. Choosing the Correct Domain**

**Given:**
$$ f(3) = -4 $$

**Options:**
- **A.** $$ (0,6) $$
- **B.** $$ (-6,-2) $$
- **C.** $$ (-\infty, \infty) $$
- **D.** $$ (-10,10) $$

**Analysis:**
The domain of a function is the set of all possible input values ($$ x $$-values) for which the function is defined. Given only the information $$ f(3) = -4 $$, we know that the function is defined at least at $$ x = 3 $$. However, without additional information about the function's behavior elsewhere, we typically assume the domain to be all real numbers unless specified otherwise.

**Answer:**  
**C.** $$ (-\infty, \infty) $$

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### **2. Determining the Set of $$ x $$-Values for $$ f(x) = -4 $$**

**Given:**
$$ f(3) = -4 $$

**Question:**  
What is the set of all $$ x $$-values such that $$ f(x) = -4 $$?

**Options:**
- **A.** $$ (0,6) $$
- **B.** $$ \{3\} $$
- **C.** $$ \varnothing $$ (the empty set)

**Analysis:**
Since $$ f(3) = -4 $$, we know that $$ x = 3 $$ is one value where $$ f(x) = -4 $$. Without additional information indicating that $$ f(x) = -4 $$ for other values of $$ x $$, the safest assumption is that $$ x = 3 $$ is the **only** solution.

**Answer:**  
**B.** $$ \{3\} $$

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### **Summary of Answers:**
1. **Correct Domain:** **C.** $$ (-\infty, \infty) $$
2. **Set of $$ x $$-Values where $$ f(x) = -4 $$:** **B.** $$ \{3\} $$
The correct domain is all real numbers, and the only $$ x $$-value where $$ f(x) = -4 $$ is $$ x = 3 $$.

Choose the correct domain.
A.
B.
C.
D.
What is the set of all -values such that
A.
B.
C.

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Solution

1. Choosing the Correct Domain

2. Determining the Set of -Values for

Summary of Answers:

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