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That's true but they have been under attack from their neighbours since the state was formed. What do their neighbours expect ?That they not defend themselves? Grossly insulting to compare their policies with that of Hitler. Why would anyone do that?

Wasn’t me, but rather likely related to calling Hitler a gentle soul in comparison to the modern ultra right Israeli leadership. That’s hyperbolic in the extreme and suggests a deep lack of moderation and measure in one’s tone…even though the current cabal under Bibi is hardly acting in ways I can support.

On what basis have you concluded that the domain is "a complex number", rather than being some portion of the set of real numbers? It should be noted, by the way, that the domain is the set of all values which *are* allowed, not the set of values which are *not* allowed.

"D = {x | x not equal to -4} Correct?" Yes. "How do I find the domain by graphing?" By drawing the graph and, in the process, noticing the vertical asymptote and thus the disallowed value. https://www.google.com/search?q=graphing+rational+functions+without+a+calculator

On the PhD level only few (<20 % decades ago) got an academic appointment. While there are private sector R&D, and similar public positions, they are also rather rare. More typical jobs are project managers, sales,product managers, tech support, etc.

My post, though joking, was a hint. So was Genadys reply. Watch the video very closely.

I have no idea why you were neg voted on this. Before someone neg reps me for asking this, let's consider Mack's assertions. Israel is indeed run by a far right coalition. The Likud Party is a RW populist and Zionist party. This is public record. And billions of dollars in US support do indeed provide some check on the party's more radical proposals. And they do indeed want to compromise the supreme courts independence from the executive and power to render decisions through a plan thinly veiled as "reform." And they have, by almost any standards, promoted a fascist shift in government and continued herding Palestinian Arabs off of their lands, shoving them into narrow and crowded strips of land and depriving them of freedoms, fundamental rights and economic access. TWIMC: Maybe knock off the neg reps and just debate the facts?

How comfortable are you with poverty? A salutary lesson for me was that I earned the same hourly rate designing drainage systems for oil refineries etc as the guys designing the most high-tech refinery units. Only while their technologies were aging, drain systems stayed as they were and I stayed employable while their speciality areas were eclipsed by more advanced technologies. If you cement yourself into a rigid specialisation in the current technological spectrum, you risk graduating into a field that is obsolete. The key exit from this trap is flexibility. I'd recommend graduating with a general technological degree and adding a BA in microeconomics or business administration. It's a crappy ladder, but every project needs a project accountant and at least you remain relevant to your field of interest even if everyone hates you. If you can show real technical abilities in the field, you have as good a chance as anyone of slipping back into the more academic realm simply by being there. It's a cynical view I know, but you do have to earn a living whilst realising your dreams.

Ironically, Israel is now run by a very far right coalition. The Israelis are only just being held in check by having to appease the US pubic opinion, without that they would make Hitler look like a gentle soul. And up to now, the courts were a moderating influence, but that's about to change.

First, let's take an example to show that sqrt{a^(2)} is not equal to a. Suppose a = -3, then: sqrt{a^(2)} = sqrt{(-3)^(2)} = sqrt{9} = 3 But a = -3, so sqrt{a^(2)} is not equal to a. Now, let's move on to explain why sqrt{a^(2)} = | a |. The square root of a number is always a positive number or zero. Therefore, when we take the square root of a square, we need to make sure that the result is also positive. In the example above, we took the square root of (-3)^2, which gave us 3. We know that the square of a number is always positive, so (-3)^2 is equal to 9. However, since a can be negative or positive, we need to use the absolute value of a to make sure that we get a positive result when we take the square root. Thus, we can conclude that sqrt{a^(2)} = | a |.

Very interesting information.

The square root may be considered a multivalued function. Example 1: a=-2 a2=+4 Example 2: a=+2 a2=4 The square operation should be applied first once a number is input to evaluate the expression. In distinction from the algebra convention when solving for variables where the power is simply removed. Squaring of course gives a positive value. Once the square root is applied, plus/minus is appended in front of the operator, for the equivalent reason absolute value is used here. ; because there is ambiguity (multi-value) output from the square root... relation. Nothing in the question remarked about limiting the domain of input or codomain of output to ensure a single-valued function.

Actually the OP described a function since it used a letter for a variable, not a specific number. It is important to distinguish between a function and the value of that function at a specific point. A square root of a number is another number, a square root of a function is another function. So a square root of 4 is 2 and another square root is -2, all of which are numbers. Folks also often make this mistake with the differential calculus, where the derived function (the derivative) has, possibly different, values at every point where the original function is differentiable.

For a given positive number, a, both x=√a and -x= -√a satisfy the equation [math]x^2= a[/math] and are called "square roots of a". The square root function, √x, however, in order to be a function, must have a single value and that is defined to be the positive value. "The" square root of x^2 is |x|.

No! Especially since you used the word "technically". Technically, [math]\sqrt{x^2}= |x|[/math]. That is x if [math]x\ge 0[/math] and -x if [math]x< 0[/math],

By convention, we refer to the major square root function when you say "THE square root." When working with real numbers, the primary square root always yields a non-negative value. Consider the two negative numbers multiplied together become a positive number, so x * x = x ^ 2 but, also, -x * -x = x^2 In most generalized questions the positive answer (x) is given, but technically -x is also an answer

a= -2. a2= 4. What is the square root of 4? (Remember that the square root is a FUNCTION so can have only one value.)

MBS, Putin, Xi… or a hundred others are taking steps like this S part of the new standard operating procedure