Given that f (x) is an even function defined on R, and f (x + 2) is an even function, then the period of F (x) is ---,. If f (63) = - 2, then f (1)=

Given that f (x) is an even function defined on R, and f (x + 2) is an even function, then the period of F (x) is ---,. If f (63) = - 2, then f (1)=

The period of solution (1) f (x) is 4. Prove: because f (x + 2) is an even function, f (- x + 2) = f (x + 2) replaces x with x + 2 to get f (- x) = f (x + 4). Because f (x) is an even function defined on R, f (- x) = f (x) so f (x) = f (x + 4), so the period of F (x) is 4 (2). Because the period of F (x) is 4, f (x) is defined on R