To find the horizontal asymptote of the function \( g(x) = \frac{1}{x} + 23 \), we need to analyze the behavior of the function as \( x \) approaches positive or negative infinity.
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As \( x \to \infty \): \[ g(x) = \frac{1}{x} + 23 \rightarrow 0 + 23 = 23 \]
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As \( x \to -\infty \): \[ g(x) = \frac{1}{x} + 23 \rightarrow 0 + 23 = 23 \]
In both cases, the function approaches 23. Therefore, the horizontal asymptote of the function \( g(x) = \frac{1}{x} + 23 \) is:
\[ y = 23 \]
Thus, the equation of the horizontal asymptote is \( \boxed{y = 23} \).