Let $\mathrm{A}=\{x \in \mathrm{R}:-1 \lt x \lt 1\}$. Which of the following is/are bijective functions from A to itself? 1. $f(x)=x|x|$ 2. $g(x)=\cos (\pi x)$ Select the correct answer using the code given below:

• Correct answer
  A

  1 only
• B

  2 only
• C

  Both 1 and 2
• D

  Neither 1 nor 2

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