Let $f: \mathbf{Q} \rightarrow \mathbf{Q}$ be a function such that $f(x+y)=f(x)+f(y)$ for all $x, y \in \mathbf{Q}$, and $f(1)=10$. Which one of the following statements is Correct ?

• A

  $f$ is surjective but not injective.
• Correct answer
  B

  $f$ is bijective.
• C

  $f$ is injective but not surjective.
• D

  $f$ is neither injective nor surjective.

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