Let f(x)= array cl -1, & -2 x < 0 x²-1, & 0 x 2 array . and g(x)=| (x)|+f(x ) . Then, in the interval (-2,2), g is:

Step-by-step solution

f(x)= array cc -1, & -2 x < 0 x²-1, & 0 x 2 array . Then, f(x )= array cc -1, & -2 |x| < 0 |x|²-1, & 0 |x| 2 array . f(|x|)=x²-1,-2 x 2 g(x)= aligned 1+x²-1, &-2 x < 0 (x²-1 )+ |x²-1 |, & 0 x 2 aligned .= array cc x², & -2 x < 0 0, & 0 x < 1 2 (x²-1 ), & 1 x 2 array .g^ (0⁻ )=0, g^ (0^ * )=0, g^ (1⁻ )=0, g^ (1⁺ )=4 g(x) is non-differentiable at x=1 g(x) is not differentiable at one point.