# Let f(x)=x|x| and g(x)=sin x.

Question:

Let $f(x)=x|x|$ and $g(x)=\sin x$.

Statement-1 : gof is differentiable at $x=0$ and its derivative is continuous at that point.

Statement-2 : gof is twice differentiable at $x=0$.

1. Statement-1 is true, Statement $-2$ is false.

2. Statement-1 is false, Statement-2 is true.

3. Statement-1 is true, Statement-2 is true; Statement- 2 is a correct explanation for Statement$1 .$

4. Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for statement$1 .$

Correct Option: 1

Solution: