Mathematics - Functions Question with Solution | TestHub

We know that any real number $x$ can be expressed as $x=\lfloor x\rfloor +\{x\}$, where $\lfloor x\rfloor$ is an integer and $0\le \{x\}<1$. We define $\lfloor x\rfloor$ as the greatest integer less than or equal to $x$, or the integral part of $x$, and $\{x\}$ as the fractional part of $x$. Suppose for any real number $x$, we write $x=\lceil x\rceil -⟨x⟩$, where $\lceil x\rceil$ is an integer and $0\le ⟨x⟩<1$. We define $\lceil x\rceil$ as the least integer greater than or equal to $x$.