The domain of definition of the function $f\left(x\right)={\left\{x\right\}}^{\left\{x\right\}}+{\left[x\right]}^{\left[x\right]}$ is (where {.} represents fractional part and [.] represents greatest integral function)

• A

  $R-I$

• B

  $R-\left[0,1\right)$

• C

  $R-\left\{I\cup \left(0,1\right)\right\}$

• D

  $I\cup \left(0,1\right)$