15 questions linked to/from Why is $\sqrt{x}$ a function?
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Why $f(x) = \sqrt{x}$ is a function?

Why $f(x) = \sqrt{x}$ is a function (as I found in my textbook) since for example the square root of $25$ has two different outputs ($-5,5$) and a function is defined as "A function from A to B is a ...
Why is $y = \sqrt{x-4}$ a function? and $y = \sqrt{4 - x^2}$ should be a circle
So why is it a function, even though for example $x = 8$; you'll have $y = +2$ and $y = -2$. It'll fail the vertical line test. But every textbook considers it as a function. Did I misunderstand ...
I know this question may be stupid but I've been studying for my test tomorrow and I'm so frustrated, I can't figure this one out. if we have a square root function like this: $y = \sqrt{x}$ wouldn't $... 3answers 113 views Why do we call things like this a function [duplicate] Why do we call$f(x) = \sqrt x$a function, if by definition$y = \sqrt x$is not a function since for included values of$x$, it gives us more than one value of$y$considering the positive and ... 0answers 70 views Question about solving$x^2 < 1[duplicate] When you have that you basically have: \begin{align*} \sqrt{x^2} & < \sqrt{1} \iff\\ |x| & < \pm 1 \end{align*} Doesn't that give you 2 options?|x| < 1, |x| <-1$? The latter is ... 5answers 2k views How can a square root be defined since it has two answers? I am aware that 1/0 is undefined for two reasons: If you would have to give an answer to this it is infinity which is not a number but a concept; The limit of 1/x for$x \to 0$is either positive or ... 5answers 6k views What is the domain and range of$y = \sqrt{9 − x^2}$? What is the domain and range of real function$f(x) = \sqrt{9 − x^2}$? In order to find the function's domain, you need to take into account the fact that, for real numbers, you can only take the ... 2answers 990 views Modulus and square root How is this statement true? "For any real number$x$we have$\sqrt{x^2} = |x|$"? Because putting$x=2\sqrt{x^2}$gives BOTH$2$and$-2$But$|x|$only gives$2$1answer 1k views Why can't you have multiple domains in one function? [duplicate] Let's say we have function$y=\sqrt x$. For natural numbers it has two solutions. For example$\sqrt 4 = \pm2$. Wouldn't it make sense then to graph a sideways parabola with more than one points in ... 5answers 201 views Implied plus-minus sign in radical equation? Say we have: $$\sqrt{x+7}=5-x$$ Is it implicitly understood that the following also holds? $$-\sqrt{x+7}=5-x$$ I'm exploring the notion of "extraneous solutions." In this example, solving either ... 2answers 84 views Is it appropriate to say that$\lim_{x \to 4}{(\sqrt x-2)}$is both$0$and$-4$? Our teachers seem to ignore that, but if I take a limit of a function with square root, for example: $$\lim_{x \to 4}{(\sqrt x-2)}$$ is it appropriate to say that there are two answers?$0$and$-4$? ... 1answer 103 views Why is it that$\sqrt{4}$is only$2$, not$\pm 2$? [duplicate] I understand that the numbers that, when squared, result in 4 are ±2 because both -2 and 2 squared result in four. However, when in a radical, why is it that$\sqrt 4$is only 2? Why isn't the sign ... 2answers 195 views 2+2=square root of 16. What's the appropriate answer? [closed] 4? Positive and negative 4? I just got into an argument with a buddy about this. He argues if it's not an i, it's not included as a imaginary number, but only the real positive number. 1answer 66 views find the equation of the tangent line to the curve$y = {\sqrt{x+2}}$at the point where$ x=2$The question asks for the equation of the tangent line. So I need this formula $$y-y_1 =m(x-x_1)$$ and the concept of derivatives $$\lim_{Δ x\to 0} \frac{f(x+Δx) - f(x)}{Δx}$$ Ok, now I have that, ... 6answers 66 views Find the range of the function$y = \sqrt{7 - x^2}\$?
I tried to find the range of the following function : $$y=\sqrt{7-x^2}$$ I found the domain which is: $$y \in (-\sqrt7,\sqrt7)$$ and then I tried to find the range of the function with the method of ...