The domain of the reciprocal function, \( f(x) = \frac{1}{x} \), is all real numbers except \( x = 0 \) (since division by zero is undefined), which can be expressed as:
Domain: \( x \in \mathbb{R}, x \neq 0 \)
The range of the reciprocal function is also all real numbers except \( y = 0 \) (since \( \frac{1}{x} \) can never equal zero for any real number \( x \)), which can be expressed as:
Range: \( y \in \mathbb{R}, y \neq 0 \)
So the complete statement is:
The domain of the reciprocal function, \( f(x) = \frac{1}{x} \), is \( x \in \mathbb{R}, x \neq 0 \), and its range is \( y \in \mathbb{R}, y \neq 0 \).
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