Let $f(x)= \dfrac{1}{1+x^2}$ and $g(x)=\dfrac{e^{−x}}{1+[x]}$, where $[x]$ is the greatest integer less than or equal to $x$. Then which of the following domain is true?
- domain of $(f+g)=R-(-2,-1]$
- domain of $(f+g)=R-[-1,0)$
- $[\text{range of f}] \cap [\text{range of g}]=\bigg[-2, \dfrac{1}{2} \bigg]$
- $[\text{range of f}] \cap [\text{range of g}]= \bigg[- \dfrac{1}{2},\dfrac{1}{2} \bigg]-\{0\}$
- Both II and IV
- Both I and III
- Both I and IV
- Both II and III