Question

How do you find the domain and range of `f(x)=1/(x+3)`?

Answer 1

`D_f =RR-{-3}.`
`R_f=RR-{0}.`

Explanation:

Remember that Division by `0` is not allowed, so, in our `f(x), x+3!=0. i.e., x!=-3`.

So, Domain of `f`, denoted by `D_f`, is `RR-{-3}.`

Also, note that, `AA x in D_f`, `f(x)!=0`, if so, then `1/(x+3)=0 rArr 1=0`, an impossibility. That gives us the Range of `f=R_f=RR-{0}.`