Question

Find the domain of the function.✓4+xf(x) =8-3xWrite your answer as an interval or union of intervals.

Answer 1

The domain is the set of possible x-values. In our case, f(x) is definined when the term into the radical is greater or equal than zero and the denominator is different from zero, that is,

$\begin{gathered} 4+x\ge0 \\ \text{and} \\ 8-3x\ne0 \end{gathered}$

From the inequality, we get

$x\ge-4$

and, from the last relation, we have

$\begin{gathered} -3x\ne-8 \\ so \\ x\ne\frac{8}{3} \end{gathered}$

By combining both results, the domain is

$\lbrack-4,\frac{8}{3})\cup(\frac{8}{3},\infty)$