Questions: What are the domain and range of the function f(x)=4 x x is a real number ;y y>0 x x>4 ;y y>0 x x is a real number; y y>4 x x>4 ;y y>4

Transcript text: What are the domain and range of the function $f(x)=4$ $\{x \mid x$ is a real number $\} ;\{y \mid y>0\}$ $\{x \mid x>4\} ;\{y \mid y>0\}$ $\{x \mid x$ is a real number\}; $\{y \mid y>4\}$ $\{x \mid x>4\} ;\{y \mid y>4$

Solution

Solution Steps

To determine the domain and range of the function $ f(x) = 4 $, we need to understand the nature of the function. The function $ f(x) = 4 $ is a constant function, meaning it outputs the same value (4) for any input $ x $.

Domain: The domain of a function is the set of all possible input values. Since $ f(x) = 4 $ is defined for all real numbers, the domain is all real numbers.
Range: The range of a function is the set of all possible output values. Since $ f(x) = 4 $ always outputs 4, the range is just the single value 4.

Solution Approach

Identify that the function is constant.
Determine that the domain is all real numbers.
Determine that the range is the single value 4.

Step 1: Identify the Domain

The function $ f(x) = 4 $ is defined for all real numbers. Therefore, the domain can be expressed as: \[ \text{Domain} = \{ x \mid x \in \mathbb{R} \} \]

Step 2: Identify the Range

Since $ f(x) = 4 $ is a constant function, it outputs the same value (4) for any input $ x $. Thus, the range is: \[ \text{Range} = \{ y \mid y = 4 \} \]

Final Answer

The domain and range of the function $ f(x) = 4 $ are: \[ \text{Domain} = \{ x \mid x \in \mathbb{R} \}, \quad \text{Range} = \{ 4 \} \] The answer is boxed as follows: \[ \boxed{\text{Domain: } \{ x \mid x \in \mathbb{R} \}, \text{ Range: } \{ 4 \}} \]

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