Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function defined by $f(x)= \begin{cases}x^2-4 x-5 & \text { if } x \geq 1, \\ 2 x & \text { if } x \lt 1 .\end{cases}$ Which one of the following statements is TRUE?

• Correct answer
  A

  $\quad f$ is onto but not one-one
• B

  $\quad f$ is one-one but not onto
• C

  $\quad f$ is neither one-one nor onto
• D

  $\quad f$ is one-one and onto

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