Question

The domain of the function $f\left(x\right)=\{x{\}}^{\left\{x\right\}}-[x{]}^{\left[x\right]}$ is:
$\left(\right[x]$ represents the greatest integer function while $\{.\}$ represents fractional part function$)$

Answer 1

Given function: $f\left(x\right)=\{x{\}}^{\left\{x\right\}}-[x{]}^{\left[x\right]}$

We know that $0^0$ is not defined.
$\left\{x\right\}=0$ for $x\in Z.$
Also, $\left[x\right]=0$ for $x\in [0,1).$
Hence, we need to exclude from the solution.

The correct domain is $R-(Z\cup (0,1))$