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 ...