Question

How do you find the domain of `f(x) = (x-4)/(x+3)`?

Answer 1

`(-oo, -3) U (-3, oo)`

Explanation:

When dealing with rational functions `f(x)=(p(x))/(q(x))` , our domain, that is, values of `x` for which `f(x)` exists, excludes any values that cause `q(x)=0.`

This is because division by `0` isn't possible, so the function won't have any real value at these values of `x`.

For `f(x)=(x-4)/(x+3),` we have the form `(p(x))/(q(x)),` where `p(x)=x-4, q(x)=x+3`

Set `q(x)=0` and solve for `x`:

`x+3=0`
`x=-3`

So, our domain excludes `x=-3`.

In interval form, the domain is

`(-oo, -3) U (-3, oo)`