Question

How do you find the domain and range of `f(x) = (2x+1) / (2x-1)`?

Answer 1

The domain is `x in RR-{1/2}`
The range is `f(x) in RR-{1}`

Explanation:

As you cannot divide by `0`, `x!=1/2`

There is a vertical asymptote `x=1/2`

Therefore,

The domain of `f(x)` is `D_(f(x))` is `x in RR-{1/2}`

`lim_(x->+-oo)f(x)=lim_(x->+-oo)(2x)/2x=1`

There is a horizontal asymptote `y=1`

The range is `f(x) in RR-{1}`

graph{(y-(2x+1)/(2x-1))(y-1)(x-1/2)=0 [-12.66, 12.65, -6.33, 6.33]}