Question

Step By Step BE VERY DETAILED with step by step as in show all work.

Answer 1

Given:

`f(x)=\sqrt[]{4-7x}`

Domain: It is the set of all input values for which the function is real or defined.

First find the non-negatives values for the radical,

`\begin{gathered} 4-7x\ge0 \\ 4\ge7x \\ (4)/(7)\ge x \\ \Rightarrow x\leq(4)/(7) \end{gathered}`

So x will take all the values less than 4/7 including 4/7. But not greater than 4/7. Because the function will not be real for x>4/7.

Answer: The domain of the function is,

`\begin{gathered} x\leq(4)/(7)\text{ or }(-\infty,(4)/(7)\rbrack \\ \end{gathered}`