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Question: Answered & Verified by Expert
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
MathematicsFunctionsAP EAMCETAP EAMCET 2018 (24 Apr Shift 1)
Options:
  • A $(0, \infty)$
  • B $R-\{0\}$
  • C $(-\infty,-1) \cup(0, \infty)$
  • D $R-\{0,-1\}$
Solution:
2184 Upvotes Verified Answer
The correct answer is: $(-\infty,-1) \cup(0, \infty)$
$\begin{array}{ll}& f(x)=\left(1+\frac{1}{x}\right)^x \\ \Rightarrow & \left(1+\frac{1}{x}\right)>0 \\ & \frac{x+1}{x}>0 \\ & \frac{-1+1}{-1} \\ \Rightarrow & x \in(-\infty,-1) \cup(0, \infty) .\end{array}$

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