Question

若f(x)是偶函数,g(x)是奇函数,且f(x)+g(x)=X³+1/X² 则f(x）=?设f(x)

Answer 1

(1)令h(x)=f(x)+g(x)=x^3+1/x^2

h(-x)=f(-x)+g(-x)=f(x)-g(x)=-x^3+1/x^2

两式相加,得：f(x)=1/x^2

(2)当x∈(-∞,0)时,-x∈(0,+∞)

∴f(x)=-f(-x)=-[(-x)(1+3√(-x))]=x(1-3√x)