Question

How do you find the domain for `f(x)=(1+3x)/(5-2x)`?

Answer 1

`(-oo,2/5)uuu(2/5,oo)`

Explanation:

The domain means anywhere where there's actually a graph. So for there to be no graph, you can't have a number which in this and pretty much all of these cases are where y goes to infinity as x progresses.
Any number divided by 0 is going to be undefined, where y goes to infinity.

So your goal is to make the denominator in that fraction a 0 so that you'll divide by it and find somewhere where the graph doesn't exist.
The algebra, then, is pretty simple.
`5-2x=0 -> 2x=5 -> x=2/5`

So then put that into the parentheses domain where the graph goes from x=infinity to 2/5 to y=infinity
`(-oo,2/5)uuu(2/5,oo)`