1.
Let the functions f:RRf: \mathbb{R} \to \mathbb{R} and g:RRg: \mathbb{R} \to \mathbb{R} be defined as:
f(x)={x+2,x<0x2,x0andg(x)={x3,x<13x2,x1f(x) = \begin{cases} x+2, & x < 0 \\ x^2, & x \geq 0 \end{cases} \quad \text{and} \quad g(x) = \begin{cases} x^3, & x < 1 \\ 3x-2, & x \geq 1 \end{cases}
Then, the number of points in R\mathbb{R} where (fg)(x)(f \circ g)(x) is NOT differentiable is equal to: