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Question
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
Options
(a) R − {0}
(b) R − {−1, 1}
(c) {−1, 1}
(d) None of these
Solution
(c) {−1, 1}
\[\text{ Let y} = \frac{x}{\left| x \right|}\]
\[\text{ For } x > 0, \left| x \right| = x\]
\[ \Rightarrow y = \frac{x}{x} = 1\]
\[\text{ For } x < 0, = - x\]
\[ \Rightarrow y = \frac{x}{- x} = - 1\]
\[\text{ Thus, range of f(x) is } { - 1, 1} .\]
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