Find the Range of the Function
Question:
Write the range of the function
\[ f(x)=e^{x-[x]}, \qquad x\in R \]
Solution:
Since
\[ 0\le x-[x]<1 \]
let
\[ t=x-[x] \]
then
\[ 0\le t<1 \]
Therefore,
\[ f(x)=e^t \]
gives
\[
1\le e^t
Hence, range is
\[
\boxed{[1,e)}
\]