if $g$ be differentiable at $a$ and $f$ non-differentiable at $f(a)$ then how is $R$?

Question

let $R(x)=f(g(x))$ and $x=a \in D_R$ now :

$1-)$ if $g$ be differentiable at $a$ and $f$ non-differentiable at $g(a)$ then how is $R$ ?

$2-)$ if $g$ be non-differentiable at $a$ and $f$ non-differentiable at $g(a)$ then how is $R$ ?

$3-)$ if $g$ be non-differentiable at $a$ and $f$ differentiable at $g(a)$ then how is $R$ ?

Answer 1

For 1: consider $g(x)=x, f(x)=|x|$ and $a=0.$

For 2: consider $g(x)=|x|, f(x)=|x|$ and $a=0.$

For 3: consider $g(x)=|x|, f(x)=x$ and $a=0.$