Question

设f(x)为奇函数,g(x)为偶函数,若f(x)-g(x)=x^2-(1/x),比较f(1),g(3),g(-2)三者的

Answer 1

f(x) - g(x) = x^2 - (1/x) (1)

因为f(x)为奇函数,g(x)为偶函数,则

f(-x) - g(-x) = (-x)^2 - (-1/x) (2)

即

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

(1) 、(3)联立解得

f(x) = - 1/x g(x) = -x^2

从而f(1) = -1,g(3) = -9,g(-2) = -4

所以

f(1)> g(-2) > g(3)