What is the Range of y=x+1/x for 0<x≤1?

[spoc21]

Homework Statement

Hello, I'm having some trouble with the following problem:

Solve y = x+\frac{1}{x} for 0 < x \leq 1

Homework Equations

y = x+\frac{1}{x} for 0 < x \leq 1

The Attempt at a Solution

I am not sure on how to start. I've spent a lot of time thinking about how to this problem, but have had no luck. The only thing comes to mind is that y = \frac{x}{x} + \frac{1}{x} = 1. This solution seems to trivial; I would greatly appreciate any help.

Thank you.

 

[Mentallic]

I'll assume the question instead means find the range of the function for the domain 0<x<1.

Are you allowed to use calculus?

I would start by finding the limit of y as x approaches 0⁺ and find y when x=1. If you can't use calculus then it will probably suffice to just explain that as x increases in that interval, y is always decreasing. This is enough information to give the range.