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

   

Answer 1

(c) {−1, 1}

\[f\left( x \right) = \frac{x}{\left| x \right|}\]

\[\text{ Let y}  = \frac{x}{\left| x \right|}\]
\[\text{ For } x > 0, \left| x \right| = x\]
\[ \Rightarrow y = \frac{x}{x} = 1\]
\[\text{ For }  x < 0, = - x\]
\[ \Rightarrow y = \frac{x}{- x} = - 1\]
\[\text{ Thus, range of f(x) is } { - 1, 1} .\]