Mathematica Mathematica Plots Wrong: How is it Possible?

[nikolafmf]

I said to Mathematica to plot a graph as this:

Plot[Exp[-Sqrt[-x]] + Exp[Sqrt[-x]] - 2 == 0, {x, -10, 40}].

You can see that there is square root of -x, which should mean that the function is defined only for x<=0. But no, Mathematica would plot a curve also for positive values of x. How is this possible at all?

 

[slider142]

Note that when x > 0, we have Exp[-Sqrt[-x]] + Exp[Sqrt[-x]] = Exp[-iSqrt[x]] + Exp[iSqrt[x]] = 2Cos[Sqrt[x]], which is defined and a real number for all real values of x > 0. The latter equality is a result of Euler's formula.