How to evaluate √|x| ? Since this function is even f(x)=f(-x), but root is not defined for negative values.

Question

I have been trying to figure out how √-x is plotted in the graph, as root is only defined for positive real values.

Answer 1

The root is only defined for non-negative real values.

However, since you are looking at the function $\sqrt{|x|}$, and the value $|x|$ is always non-negative, that shouldn't cause too much of a problem.

When plotting the function, you might want to remember that if a function is even, then its graph is symmetric across the y axis. So you can only draw the plot for $x>0$, then mirror it over the y axis to get the full plot.

Answer 2

Since $|x| \ge 0$, the function $f(x)=\sqrt{|x|}$ is defined for all $x$.

For $x <0$ we have $|x|=-x$, hence $f(x)=\sqrt{-x}.$

Answer 3

Yes, $\sqrt{x}$ is only defined for non-negative values of x (positive x and 0). But aren't you asking about $\sqrt{|x|}$? If $x= -4$ then $|x|= 4$ so $\sqrt{|x|}= 2$.