The function $g(x) = \begin{cases} x + b, & x < 0 \\ \cos x, & x \geqslant 0 \end{cases}$ can be made differentiable at $x = 0$.

Let $f(x) = 15 - |x - 10|; x \in R$. Then the set of all values of $x$,at which the function $g(x) = f(f(x))$ is not differentiable,is

If $f(x) = \begin{cases} 2a - x & \text{when } -a < x < a \\ 3x - 2a & \text{when } a \leq x \end{cases}$,then which of the following is true?

The set of all points,where the derivative of the function $f(x) = \frac{x}{1+|x|}$ exists,is

Let $f : R \to R$ be differentiable at $c \in R$ and $f(c) = 0$. If $g(x) = |f(x)|$,then at $x = c$,$g$ is

For the function $f(x) = e^{\sin |x|} - |x|$, $x \in R$, consider the following statements:
Statement $I$: $f$ is differentiable for all $x \in R$.
Statement $II$: $f$ is increasing in $(-\pi, -\frac{\pi}{2})$.
In the light of the above statements, choose the correct answer from the options given below: