Question

Prove that f(x)=x+1/x is increasing on [1,infinity).

Answer 1

A function f(x) is said to be a strictly increasing function on (a,b) if
x1<x2⇒f(x1)<f(x2) for all x1,x2∈(a,b)

Now take x1 and x2 as 2 and 3
2<3-----------------ie x1<x2

now f(2) = 2+1/2 = 5/2= 2.5
f(3) = 3+1/3 = 10/3 = 3.33

So clearly f(x1)<f(x2)
so we can say that f(x)=x+1/x is increasing on [1,infinity)
You can another set of a and b to confirm.