1.奇偶性例1若f(x+y)=f(x)+f(y),判断f(x)的奇偶性.解令x=y=0,得f(0)=0,令y=-x,得f(x-x)=f(x)+f(-x),所以f(0)=f(x)+f(-x),又f(0)=0,故f(-x)=-f(x),因为f(x)不恒为0,所以f(x)是奇函数.例2已知函数y=f(x)(x∈R,x≠0),对任意非零实数x_1,x_2都有f(x_1x_2)=f(x_1)+f(x_2),试判断f(x)的奇偶性.解令x_1=-1,x_2=1,得 1. Parity Example 1 Determine the parity of f (x) if f (x + y) = f (x) + f (y). Let x = y = 0 and let f so that f (x) = f (x) + f (-x) so that f (0) = f (x) + f f (x) = - f (x), f (x) is an odd function because f (x) is not always 0. Example 2 The function y = f For any nonzero real number x_1, x_2 has f (x_1x_2) = f (x_1) + f (x_2), try to judge the parity of f (x). Let x_1 = -1, x_2 = 1