Let `f(x)={(x+a if x lt 0), (|x-1| if x ge 0):}` and `g(x)={(x+1 if x lt 0), ((x-1)^2+b if x ge 0):}`, where a and b are non-negative real numbers. Determine the composite function gof. If (gof) (x) is continuous for all real x, determine the values of a and b. Further, for these values of a and b, is gof differentiable at x = 0?

Explanation

Hence, `gof(x)={(x+2, if x lt -1), (x^2, if -1 le x lt 0), ((|x-1|-1)^2, if x ge 0):}` a = 1 and b = 0