what is the range of the function f(x)=1/root(|x|-x) and its domain.

Answer 1

√(|x| - x) is defined only for |x|-x ≥ 0

if x=0, f(0) is undefined
if x > 0 , |x| - x = 0 , so f(x) is undefined
if x < 0 , |x| - x = -2x , e.g x = -5 , then
|-5| -(-5) = 10

so domain of x is x < 0
range is y > 0

e.g. let x = -.00001 , f(-.00001) = 223.6
as x gets closer to -0 f(x) gets larger +
let x = -10000 , f(-10000) = .00707..
as x ---> -∞ , f(x) ---> 0