Question 1026406
1.  {{{y = sqrt(f(x)) = sqrt(2x^2-6)}}} would have the domain {{{2x^2 - 6 >=0}}}, or ({{{-infinity}}}, {{{-sqrt(3)}}}]∪[{{{sqrt(3)}}}, {{{infinity}}}).  Incidentally the smallest value of y happens when x = {{{-sqrt(3)}}} or x = {{{sqrt(3)}}}. So the answer to your question is {{{sqrt(3)}}}, approximately 1.73 to nearest hundredth.

2.  The "endpoint" of the graph of {{{y=4sqrt(2-x)+3}}} happens when x = 2, which is the minimum point of the graph.  The corresponding y-value is y = 3.