Linked Questions

14
votes
2answers
8k views

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 ...
4
votes
3answers
11k views

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 ...
2
votes
3answers
126 views

Question about the graph of the square root function [duplicate]

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 $...
-2
votes
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 ...
0
votes
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 ...
4
votes
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 ...
0
votes
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 ...
3
votes
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 $2$
0
votes
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 ...
3
votes
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 ...
1
vote
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 $-4$? ...
4
votes
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 ...
-2
votes
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.
2
votes
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, ...
0
votes
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 ...