Mathematics - Functions Question with Solution | TestHub

If $\mathrm{f}(\mathrm{x})={\log }_{100\mathrm{x}}\left(\frac{2\left({\log }_{10}\mathrm{x}\right)+2}{-\mathrm{x}}\right),\mathrm{g}(\mathrm{x})=\{\mathrm{x}\}$ where $\}$ denotes the fractional part of x , then range of $\mathrm{g}(\mathrm{x})$ for existence of $\mathrm{fog}(\mathrm{x})$ is