Question

How do you find the domain and range of `g(x)=6/(3-5x)`?

Answer 1

The domain is `D_g(x)=RR-{3/5}`
The range is `R_g(x)=RR-{0}`

Explanation:

`g(x)=6/(3-5x)`

As we cannot divide by `0,`, `x!=3/5`

The domain of `g(x)` is `D_g(x)=RR-{3/5}`

`lim_(x->-oo)g(x)=lim_(x->-oo)6/(-5x)=0^+`

`lim_(x->+oo)g(x)=lim_(x->+oo)6/(-5x)=0^-`

The range of `f(x)` is `R_g(x)=RR-{0}`