AP EAMCET · Maths · Functions
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
- A \((0, \infty)\)
- B \(R-\{0\}\)
- C \((-\infty,-1) \cup(0, \infty)\)
- D \(R-\{0,-1\}\)
Answer & Solution
Correct Answer
(C) \((-\infty,-1) \cup(0, \infty)\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll}& f(x)=\left(1+\frac{1}{x}\right)^x \\ \Rightarrow & \left(1+\frac{1}{x}\right)>0 \\ & \frac{x+1}{x}>0 \\ & \frac{-1+1}{-1} \\ \Rightarrow & x \in(-\infty,-1) \cup(0, \infty) .\end{array}\)
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