$[\mathrm{t}]$ denotes the greatest integer function and $[\mathrm{t}-\mathrm{m}]=[\mathrm{t}]-\mathrm{m}$ when $\mathrm{m} \in \mathrm{Z}$. If $\mathrm{k}=2[2 \mathrm{x}-1]-1$ and $3[2 \mathrm{x}-2]+1=2[2 \mathrm{x}-1]-1$ then the range of $\mathrm{f}(\mathrm{x})=$ $[\mathrm{k}+5 \mathrm{x}]$ is

• A

  $\{7,8,9\}$
• B

  $\{4,5,6\}$
• C

  $\{5,6,7\}$
• Correct answer
  D

  $\{6,7,8\}$

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