Find the Range of the Function
Question:
The range of the function
\[ f(x)=\frac{x}{|x|} \]
is
(a) \(R-\{0\}\)
(b) \(R-\{-1,1\}\)
(c) \(\{-1,1\}\)
(d) none of these
Solution:
If \(x>0\),
\[ \frac{x}{|x|}=1 \]
If \(x<0\),
\[ \frac{x}{|x|}=-1 \]
Therefore, possible values are
\[ \{-1,1\} \]
Hence, the range is
\[ \boxed{\{-1,1\}} \]
\[ \boxed{\text{Correct Answer: (c)}} \]