Question

Find the domain of f and write your answer in interval notation.f(x)=3√(6−5x)+4

Answer 1

We will have the following:

First, we are given:

`f(x)=3√(6-5x)+4`

Now, to determine the domain we calculate for which value the root is 0, that is:

`\begin{gathered} √(6-5x)=0\Rightarrow5x-6=0 \\ \Rightarrow5x=6\Rightarrow x=(6)/(5) \end{gathered}`

Now, any value greater then 6/5 will make the expression have imaginary solutions, so the domain of the expression will be:

`Dom_f=(-\infty,6/5\rbrack`

This, can be seeing as follows: