Question

Let the functions : (−1,1) → R and g : (−1,1) → (−1,1) be defined by 

f(x) = |2x − 1| + |2x + 1| and g(x) = x − [x], 

Where [x] denotes the greatest integer less than or equal to x. Let fo:(−1,1) → R be the composite function defined by (fog)(x) = f(g(x)). Suppose c is the number of points in the interval (−1,1) at which fog is NOT continuous, and suppose d is the number of points in the interval (−1,1) at which fog is NOT differentiable. Then the value of c + d is _____ 

Answer 1

f(x) = |2x – 1| + |2x + 1| 

g(x) = {x} 

f(g(x)) = |2{x} – 1| + |2{x} + 1|