若f(x)=ax+bsin^3x+3,且f(-3)=7,则f(3)的值

问题描述:

若f(x)=ax+bsin^3x+3,且f(-3)=7,则f(3)的值

令g(x)=f(x)-3=ax+bsin^3x
g(x)+g(-x)=0 (奇函数)
g(-3)+g(3)=0
=>f(-3)-3+f(3)-3=0
=>f(3)=6-7=-1