F(x+2) is an even function, so the symmetry axis of F(x) is x =-2, and fx itself is odd function, so f0 is equal to 0. Then use the symmetry axis, F0 = f-4 =-f4, f4 and f-6 are symmetric, f6 is equal to 0, f6 and f-8 are symmetric f8 is equal to 0, and then f 1 and f-3 are symmetric f3. . . Through the above analysis, the period is twice the distance from the symmetry axis to the origin of odd function.