The function $f :N\to I$ defined by $f\left(x\right)=x-5\left[\frac{x}{5}\right]$ , where $N$ is the set of natural numbers and $\left[x\right]$ denotes the greatest integer less than or equal to $x$, is:

• A

  one-one but not onto
• B

  one-one and onto
• Correct answer
  C

  neither one-one nor onto
• D

  onto but not one-one

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