Is the domain all real numbers?
Understand the Problem
The question is asking whether the domain of a certain function includes all real numbers. To answer this, we would need to identify the specific function in question and analyze its properties to see if there are any restrictions on the input values.
Answer
The domain depends on the specific function analyzed. For instance, $g(x) = \frac{1}{x}$ has a domain of $(-\infty, 0) \cup (0, \infty)$.
Answer for screen readers
The answer depends on the specific function in question. For example, the domain of $f(x) = \sqrt{x}$ is $[0, \infty)$, while the domain of $g(x) = \frac{1}{x}$ is $(-\infty, 0) \cup (0, \infty)$.
Steps to Solve
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Identify the function You need to determine the function whose domain you are analyzing. For example, if it is $f(x) = \sqrt{x}$, you will need to consider the properties of square roots.
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Analyze input values Examine whether there are any restrictions based on the function's behavior. For example, if your function involves a square root, the expression under the root must be non-negative.
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Determine the domain Based on your analysis, state the set of all possible input values. For the function $g(x) = \frac{1}{x}$, the domain is all real numbers except $x = 0$.
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Summary of findings Conclude whether the domain includes all real numbers or if there are specific exclusions. If your function has no restrictions, then the domain is the set of all real numbers, written as $(-\infty, \infty)$.
The answer depends on the specific function in question. For example, the domain of $f(x) = \sqrt{x}$ is $[0, \infty)$, while the domain of $g(x) = \frac{1}{x}$ is $(-\infty, 0) \cup (0, \infty)$.
More Information
Understanding the domain of a function is crucial in mathematics because it determines the values that can be inputted into the function without resulting in undefined outcomes.
Tips
- Assuming the domain includes all real numbers without analyzing the function's properties.
- Overlooking restrictions that result from operations like division by zero or taking square roots of negative numbers.
