Given that the image of the function f (x) defined on R is symmetric with respect to the point (- 3 / 4,0) and satisfies f (x) = - f (x + 3 / 2). F (- 1) = 1. F (o) = - 2, then the value of f (1) + F (2) + F (3) +... + F (2008) is () A.-2 B.-1 C.0 D.1

Given that the image of the function f (x) defined on R is symmetric with respect to the point (- 3 / 4,0) and satisfies f (x) = - f (x + 3 / 2). F (- 1) = 1. F (o) = - 2, then the value of f (1) + F (2) + F (3) +... + F (2008) is () A.-2 B.-1 C.0 D.1

F (x) = - f (x + 3 / 2) replace x with x + 3 / 2 and substitute f (x + 3 / 2) = - f (x + 3). Then we know that f (x) = f (x + 3) is a function with period 3. F (- 1) = 1 = f (2) = f (5) =... F (0) = - 2 = f (3) =. Note that the odd function has f (- x) = - f (x) with respect to (0,0) symmetry, and this function has f (- x-3 / 2) = - f (x) with respect to (- 3 / 4,0) symmetry