Question

What is the domain and range of `(5x-3)/(2x+1)`?

Answer 1

The domain is `D_f(x)=RR-{-1/2}`
The range is `R_f(x)=RR-{5/2}`

Explanation:

Let `f(x)=(5x-1)/(2x+1)`

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

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

`lim_(x->+-oo)f(x)=lim_(x->+-oo)(5x)/(2x)=5/2`

The range of `f(x)` is `R_f(x)=RR-{5/2}`