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The set of all real values of $x$ for which the real valued function $f(x)=\left(1+\frac{1}{x}\right)^x$ is defined, is
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$(-\infty,-1) \cup(0, \infty)$
$\begin{array}{ll}& f(x)=\left(1+\frac{1}{x}\right)^x \\ \Rightarrow & \left(1+\frac{1}{x}\right)>0 \\ & \frac{x+1}{x}>0 \\ & \frac{-1+1}{-1} \\ \Rightarrow & x \in(-\infty,-1) \cup(0, \infty) .\end{array}$
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