The monotonicity of the function is used to find the range of f (x) = x+1/x. If the school talks about the check function, it will be easier and drawing can solve it. Otherwise, you have to prove it yourself. When x>0, f(x)=x+ 1/x has a monotonic increasing interval of 1,+infinity) and a decreasing interval of (0, 1), so f(x) reaches the minimum at x= 1. 2.f (x) >: =2 Because f (x) is odd function, the image is symmetrical about the origin. So when x

Increase+decrease, decrease+increase can't judge monotonicity.

The law of Ff(x) is "the same increase but different decrease". When finding the monotone interval of a composite function, first find the definition domain of the composite function, then decompose it into several simple functions, discuss the monotone interval of the simple functions on the definition domain respectively, and then judge the monotonicity of the composite function by "increasing the same while decreasing the same"