Question

How do you find the domain of `f(x) = (2x)/(2x-5)`?

Answer 1

The domain of `f(x)` is `(-oo, 5/2)uu(5/2, +oo)`

Explanation:

`f(x) = (2x)/(2x-5)`

`f(x)` is defined for all x except where `2x-5=0`
`:.f(x)` is defined `forall x in RR: x!=5/2`

Thus the domain of `f(x)` is `(-oo, 5/2)uu(5/2, +oo)`

We can see this from the graph of `f(x)` below.

graph{2x/(2x-5) [-7.89, 14.61, -4.575, 6.665]}