Here's my situation. I have a set theory background so I'm out of my league in applied, computational methods so I'd appreciate a hand-up.
I have a set of five functions, $f_{i}(x) \ $ where $\ 0 < x < 1$. They are all of the form: $$f_{i}(x) = \frac{a_{i}}{ b_{i}x + c_{i}}$$ where all a, b, c are constant and positive real numbers.
I also have a version of each function, call it $$f^{round}_{i} = \frac{a_{i}}{ round(b_{i}x) + c_{i}}$$ where the only difference is that bx is rounded in calculation.
Is there a numerical method to find ranges of values of x such that given $\epsilon > 0 \ \forall i <=5 \ \ |f^{round}_{i}(x) - f_{i}(x)| < \epsilon$?
Single values of x would also be fine.