TS EAMCET · Maths · Functions
The range of the real valued function \(f(x)=\frac{1}{x-|x|}\) is
- A \((0, \infty)\)
- B \((-\infty, 0)\)
- C \((-\infty, 0) \cup(0, \infty)\)
- D \((-\infty, \infty)\)
Answer & Solution
Correct Answer
(B) \((-\infty, 0)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{1}{x-|x|}\) For \(x \geq 0, x-|x|=0 \Rightarrow {f}({x}) \rightarrow \infty\) \(\begin{array}{ll}\therefore & x < 0,|x|=-x \\ \Rightarrow & f(x)=\frac{1}{2 x} \\ \therefore & \text { Range } \in(-\infty, 0)\end{array}\)
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