Questions: What are the domain and range of this function?

What are the domain and range of this function?
Transcript text: What are the domain and range of this function?
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Solution

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Solution Steps

Step 1: Identify the Domain

The domain of the function \( f(x) = x^2 \) is the set of all possible input values for which the function is defined. Since \( f(x) \) is a polynomial function, it is defined for all real numbers. Therefore, the domain can be expressed as: \[ \text{Domain} = \mathbb{R} \]

Step 2: Identify the Range

The range of the function \( f(x) = x^2 \) is the set of all possible output values that the function can produce. Since the output of \( f(x) \) is always non-negative (i.e., \( f(x) \geq 0 \) for all \( x \)), the range is: \[ \text{Range} = [0, \infty) \]

Final Answer

\[ \text{Domain: } \boxed{\mathbb{R}} \quad \text{Range: } \boxed{[0, \infty)} \]

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