Question

For which values of x does each expression make sense? √(-2x)^2

Answer 1

We want to see for which values of x does the rational expression make sense. We will see that the expression makes sense for x ≤ 0

We know that the argument of a square root can only be a real number equal to or larger than zero.

In this case, we have the expression:

$\sqrt{(-2x)^2} = (\sqrt{-2x} )^2$

One would want to directly cancel the square root with the 2 exponent, but we can't do that, because in the right-side expression we would have a complex number if the argument is smaller than zero.

The first thing we need to do is to make the argument equal or larger than zero:

-2x ≥ 0

x ≤ 0/-2

x ≤ 0

So the given expression only makes sense for x ≤ 0

If you want to learn more about rational expressions, you can read:

https://brainly.com/question/18545256