Question

若函数f(x)=ax^2+bx+c是偶函数,则g(x)=ax^3+bx^2+cx是

Answer 1

f(x)=ax^2+bx+c

f(-x)=ax^2-bx+c

f(x)是偶函数

则f(x)=f(-x)

得b=0

g(x)=ax^3+bx^2+cx

=ax^3+cx

g(-x)=-ax^3-cx

g(x)=-g(-x)

g(x)为奇函数