Question 134220
{{{sqrt(2x+5)}}} Start with the given expression


Remember you cannot take the square root of a negative value. So that means the argument {{{2x+5}}} must be greater than or equal to zero (i.e. the argument <font size=4><b>must</b></font> be nonnegative)


{{{2x+5>=0}}} Set the inner expression greater than or equal to zero


{{{2x>=0-5}}}Subtract 5 from both sides



{{{2x>=-5}}} Combine like terms on the right side



{{{x>=(-5)/(2)}}} Divide both sides by 2 to isolate x 




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=sqrt(2x+5)}}} , we get

{{{ graph( 500, 500, -10, 10, -10, 10, sqrt(2x+5)) }}} 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