Given:
[tex]f(x)=\sqrt[]{4-7x}[/tex]
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,
[tex]\begin{gathered} 4-7x\ge0 \\ 4\ge7x \\ \frac{4}{7}\ge x \\ \Rightarrow x\leq\frac{4}{7} \end{gathered}[/tex]
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,
[tex]\begin{gathered} x\leq\frac{4}{7}\text{ or }(-\infty,\frac{4}{7}\rbrack \\ \end{gathered}[/tex]
