Let $\mathrm{R}$ be the set of real numbers and $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be defined by $f(x)=\frac{\{x\}}{1+[x]^{2}}$, where $[x]$ is the greatest integer less than or equal to $\mathrm{x}$, and $\{x\}=x-[x] .$ Which of the following statements are true ? I. The range of $f$ is a closed interval II. $\mathrm{f}$ is continuous on $\mathrm{R}$. III. $\mathrm{f}$ is one-one on $\mathrm{R}$.

• A

  I only
• B

  II only
• C

  III only
• Correct answer
  D

  None of I, II and III

Hence, the correct answer is option: 'D'.