If $f: R \rightarrow R$ is defined as $f(x)=|x+1|+|x-1|$, then $f(x)$ is

Which of the following statements is not true?

Assertion $(A)$: $f(x) = |x|$ is differentiable at $x = a \neq 0$ and continuous but not differentiable at $x = 0$.
Reason $(R)$: If a function is differentiable at a point,then it is continuous at the point. But the converse is not true.

If $f(x) = \begin{cases} \frac{x^2 \ln \cos x}{\ln (1+x^2)} & , x \neq 0 \\ 0 & , x=0 \end{cases}$, then $f(x)$ is

The domain of the derivative of the function $f(x) = \frac{x}{1+|x|}$ is

If $f(x) = \begin{cases} \frac{1}{|x|}, & |x| \geq 1 \\ ax^2 + b, & -1 < x < 1 \end{cases}$ is differentiable $\forall x \in \mathbb{R}$,then one of the values of $a$ and $b$ is-