Find the range of the function , $\displaystyle f(x)=-e^{-2x}+2e^{-x}+1$ , x is real and x>0

Attempt :

$\displaystyle f(x)=-\frac{1}{e^{2x}}+\frac{2}{e^x}+1$

so when x=0 , f(x)=2

and when x approaches infinity , f(x) converges to 1 .

the range would be [1,2)

is this acceptable ?