Mathematics · Continuity and Differentiability

Let α ∈ R be such that the function f(x) defined below is continuous at x = 0, where {x} denotes the fractional part function x - [x], and [x] is the greatest integer function. Then: f(x) = cos-1(1 - {x}2) sin-1(1 - {x}){x} - {x}3 for x ≠ 0, and f(0) = α.