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