Question

function... find the domain, see attached

Answer 1

The domain is all the values you can put in the function f(x) and get a return value

recall when the square root function is defined

Answer 2

See the square root function is only defined for x=0 and larger. So the stuff under a root sign must be greater than or equal to zero...
here it is -9x + 4

Answer 3

\[-9x+4 \ge 0\]
solving
\[x \le \frac{ 4 }{ 9 }\]

That sets a restriction on the domain values on the domain