Find the Range of the Function
Question:
The range of the function
\[ f(x)=\frac{x+2}{|x+2|}, \qquad x\ne-2 \]
is
(a) \(\{-1,1\}\)
(b) \(\{-1,0,1\}\)
(c) \(\{1\}\)
(d) \((0,\infty)\)
Solution:
If \(x+2>0\),
\[ \frac{x+2}{|x+2|}=1 \]
If \(x+2<0\),
\[ \frac{x+2}{|x+2|}=-1 \]
Therefore, possible values are
\[ \{-1,1\} \]
Hence, the range is
\[ \boxed{\{-1,1\}} \]
\[ \boxed{\text{Correct Answer: (a)}} \]