KCET · Maths · Functions
Domain of \(f(x)=\frac{x}{1-|x|}\) is
- A \(R-[-1,1]\)
- B \((-\infty, 1)\)
- C \((-\infty, 1) \cup(0,1)\)
- D \(R-\{-1,1\}\)
Answer & Solution
Correct Answer
(D) \(R-\{-1,1\}\)
Step-by-step Solution
Detailed explanation
Given function,
\(f(x)=\frac{x}{1-|x|}\)
\(\because\) Denominator can't be zero.
\(\begin{array}{lc}
\therefore & 1-|x| \neq 0 \\
\Rightarrow & |x| \neq 1 \\
\Rightarrow & x \neq \pm 1
\end{array}\)
Hence, domain is \(R-\{-1,1\}\).
\(f(x)=\frac{x}{1-|x|}\)
\(\because\) Denominator can't be zero.
\(\begin{array}{lc}
\therefore & 1-|x| \neq 0 \\
\Rightarrow & |x| \neq 1 \\
\Rightarrow & x \neq \pm 1
\end{array}\)
Hence, domain is \(R-\{-1,1\}\).
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