Question
What is the domain and range of the function \( f(x)=\frac{1}{x} \) ? Express your answer in interval notation. Domain: Range:
Ask by Edwards Mcfarlane. in the United States
Nov 22,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
Domain: \( (-\infty, 0) \cup (0, \infty) \)
Range: \( (-\infty, 0) \cup (0, \infty) \)
Solution
Analyze the range of the function \( f(x)=\frac{1}{x} \).
Function by following steps:
- step0: Find the range:
\(f\left(x\right)=\frac{1}{x}\)
- step1: Evaluate:
\(f\left(x\right)\neq 0\)
The domain of the function \( f(x)=\frac{1}{x} \) is all real numbers except 0, which can be expressed in interval notation as \( (-\infty, 0) \cup (0, \infty) \).
The range of the function \( f(x)=\frac{1}{x} \) is all real numbers except 0, which can be expressed in interval notation as \( (-\infty, 0) \cup (0, \infty) \).
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Simplify this solution Bonus Knowledge
The domain of the function \( f(x) = \frac{1}{x} \) includes all real numbers except for \( x = 0 \), where the function is undefined. In interval notation, this can be expressed as \( (-\infty, 0) \cup (0, \infty) \). As for the range, since the function outputs all real numbers except for zero (it approaches but never reaches it), the range is also expressed in interval notation as \( (-\infty, 0) \cup (0, \infty) \). Both the domain and range reflect how the graph of \( f(x) \) resembles a hyperbola that never intersects the x-axis or y-axis.
