Let x=x-2 be substituted to get f(x)=f(-x+2).

∴f(x) is symmetrical about the straight line x= 1;

f(x+2)=-f(x)

Let x=x+2 be substituted to get f(x+4)=-f(x+2)=f(x).

∴f(x) is a periodic function with a minimum positive period of 4;

f(x+2)=-f(-x)

f(x+ 1)= [ 1/f(x)]

Let x=x+ 1 substitute f (x+2) =1/f (x+1) = f (x).

∴f(x) is a periodic function with a minimum positive period of 2;

f(x+3)=f(-x+5)

Substitute x=x-3 to get f(x)=f(-x+8).

∴f(x) is symmetrical about the straight line x=4;

f(x+3)=f(x+5)

Substitute x=x-3 to get f(x)=f(x+2).

∴f(x) is a periodic function with a minimum positive period of 2;