Question 142579


{{{2*sqrt(4x+10)}}} Start with the given expression


Remember you cannot take the square root of a negative value. So that means the argument {{{4x+10}}} must be greater than or equal to zero 



{{{4x+10>=0}}} Set the inner expression greater than or equal to zero


{{{4x>=0-10}}}Subtract 10 from both sides



{{{4x>=-10}}} Combine like terms on the right side



{{{x>=(-10)/(4)}}} Divide both sides by 4 to isolate x 




{{{x>=-5 / 2}}} Reduce



So that means x must be greater than or equal to {{{-5 / 2}}} in order for x to be in the domain


So the domain in set-builder notation is

*[Tex \LARGE \textrm{\left{x|x\ge -\frac{5}{2}\right}}]


So here is the domain in interval notation: [{{{-5 / 2}}},*[Tex \LARGE \infty])




Notice if we graph {{{y=2*sqrt(4x+10)}}} , we get

{{{ graph( 500, 500, -10, 10, -10, 10, 2*sqrt(4x+10)) }}} notice how the graph never crosses the line {{{x=-5 / 2}}}. So this graphically verifies our answer.


and we can see that x must be greater than or equal to {{{-5 / 2}}} in order to lie on the graph