f(x)=ax{5次方}+bx{3次方｝＋cx+5,且f(-3)=3,求f(3)

题目

f(x)=ax{5次方}+bx{3次方｝＋cx+5,且f(-3)=3,求f(3)

答案

f(x)=ax^5+bx^3+cx+5
设g(x)=ax^5+bx^3+cx
g(-x)=-(ax^5+bx^3+cx)=-g(x)
g(x)是奇函数
f(-3)=g(-3)+5
f(3)=g(3)+5
两式相加
3+f(3)=10
f(3)=7