Question

定义函数f(x)=max(x^2,x^-2)x∈(-∞,0)∪(0,+∞)求f(x)的最小值

Answer 1

令x^2≥x^-2,化简

x^2-x^-2≥0

x^4-1≥0

(x^2-1)(x^2+1)≥0

x^2-1≥0

(x-1)(x+1)≥0

x≤-1或x≥1

也就是说,当x≤-1或x≥1时,x^2≥x^-2,所以f(x)=max(x^2,x^-2)=x^2

同理可得,当-1≤x