Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions such that
$g \circ f(x)= \begin{cases}x^2, & \text { if } x \geq 0 \\ e^x-1, & \text { if } x \lt 0\end{cases}$
Then which of the following statements is correct?

• A

  $g$ is onto.
• B

  $f$ is onto.
• Correct answer
  C

  $f$ is one-one.
• D

  $g$ is one-one.

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