Question

急f(x)为奇函数,g(x)为偶函数,且f(X)+g(X)=a的x次幂,证明：f(2x)=2f(x)乘以g(x)

Answer 1

f(x)+g(x)=a(x)

f(-x)+g(-x)=a (-x)

-f(x)+g(x)=a(-x)

g(x)=(a(x)+a(-x))/2

f(x)=(a(x)-a(-x))/2

2f(x)g(x)=(a(x2)-a(-x2))/2=f(2x)

写的急了点,希望有用