Image of Function h: (0,1)→ ℝ - 65 characters

[mrchris]

Homework Statement

find the image of the function
h: (0,1)→ ℝ defined by h(x) = 1/(x²+8x) for 0<x<1

Homework Equations

The Attempt at a Solution

I have tried a number of things, I can see the answer intuitively but I am having trouble with the proof. I set the function up as 1/(x²+8x)=b, and I have been trying to manipulate this in order to get what I need. the first thing i did was calculate b at x=0 (undefined) and x=1 (1/9) and from there I got 3 different intervals for b, the last one (1/9, ∞) i know is correct. I just am not sure how to show this is correct.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Here is one basic fact you need here- the fraction f(x)/g(x) is equal to 0 if and only if the numerator, f(x), is 0.