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Question
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
Options
(a) {−1, 1}
(b) {−1, 0, 1}
(c) {1}
(d) (0, ∞)
Solution
(a) {−1, 1}
\[\text{ For } \left| x + 2 \right| > 0, \]
\[\text{ or } x > - 2 , \]
\[y = \frac{x + 2}{x + 2} = 1\]
\[\text{ For } \left| x + 2 \right| < 0, \]
\[\text{ or } x < - 2, \]
\[y = \frac{x + 2}{- (x + 2)} = - 1\]
\[\text{ Thus } , y = { - 1, 1}\]
\[\text{ or range } f(x) = { - 1, 1} .\]
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