Domain Definition and 743 Threads

Homework Statement A problem in my textbook gives the domain of sec x as [0,(pi/2)) U ((pi/2), pi]. This makes perfect sense of course. However, it is asking for an alternate domain. I've looked at the graphs of both sec x and arcsec x to try to figure out a different domain for sec x(I looked...

I was wondering if there's any symbol i could use for the domain of this question f(x) = (2x^2 + 25)^(0.5) + 1 as we can see that , f(x) will always be greater or equal to zero , was wondering what would the domain be ? Could anyone help me out ? thanks

When asked to find the domain, what bracket is used to denote that a number is excluded or included in the domain, ( or [?

I was just going through some problems in a maths journal for undergraduate level i found a sum seeming simple but i am not able to solve it completely find domain of \sqrt{x^{12} - x^9 + x^4 -x +1}i know domain includes all negative value , all positive value >1 , but i can't get anything...

I'm currently self-studying ODE, text by Morris Tenenbaum, and I am confused by these 2 problems. z=\sqrt{-(x^2 + y^2)} D: (0,0) z=\sqrt{-(x^2 + y^2 +1)} undefined

http://www.math.yorku.ca/Who/Faculty/Kochman/M1300/solutions/solF04/SFE.pdf Question 2. I agree that the range of arctan is [-pi/2, pi/2], however due to the fact that we have arctan(2x), not just arctan(x), wouldn't that mean that the range of the g(x) function would be [-pi/4, pi/4]...

Homework Statement how to find the domain of an vector function? Homework Equations The Attempt at a Solution

Please Help with Domain... Homework Statement For f(x) Determine Domain, Vertical Asymptote and x and y intercepts. then State and graph the effect of the modifications and sketch the graph of f(x) Given f(x) = - log3(x – 1) + 2 For g(x) determine domain, Horizontal asymptote and x...

heres a question I am trying to figure out if this equations domain f(t)=4.5e^t where e is 2.1783 im thinking that the answer is all positve numbers. because it can't equal zero so all negative numbers cause it to be 0

Can someone please tell me why the domain of y=2x^2+12x+12 is x elementof IR

I'm having a bit of trouble grasping the domain and range of functions of 2 variables. Does anyone know of any helpful tutorials that will help me get the hang of this concept? Any help appreciated.

i have this question that i don't totally get what it wants exactly so if anyone can help me understand it correctly, thx Find the natural domain of the function algebraically,and confirm that your result is consistent with the graph produced by your graphing utility. note: set your graphing...

I was just wondering if you could write a functions domain and range with a set? Would it be something like D: {x \epsilon \mathbb{R} | any condtitions} R: {f(x) \epsilon \mathbb{R} | any condtitions} for any function f(x)?

1. Find the domain of the function 5x/8x^2+9 in interval notation. 2. 3. I believe the domain is all real numbers, but do not know what that would look like in interval notation. Could someone show me?

Homework Statement if f\left( x\right) :=\frac{1}{x-1} for f(x) Doman (x != 1) g\left( x\right) :=\frac{1}{\sqrt{x+1}} for g(x), Domain (x >= -1) so for f(g(x)) the Domain would be (-1,0) U (0, inf)? or do I need to consider other things?

Can anyone explain how to get the domain of f(x)=ln(ln(ln(x)))? I am stuck at e^lnlnx > e^o... Thank you.

¿Could the domain of a compound function be obtained in the same way that non-compound functions? I think the answer is not, like in this example: f(x)=1/x² g(x)=√(2x-6) f(g(x))=1/(√(2x-6))² Recently Hurkyl explained me that (a^b)^c is not always equal to a^bc, although, I've proved this...

In my book and in other places, they give this rule to obtain the domain for a compound function: "the domain of (f o g) (x) is the set of all real numbers x such that g(x) is in the domain of f (x)." Then, if f(x)=x^(1/4) and g(x)=x^2 f(g(x)) = (x^2)^(1/4) f(g(x)) = x^(1/2) And applying...

Find the domain & range of the function. 2x^2 + 4x - 3 I attempted to solved doing the following 2x^2 + 4x = 3 x^2 + 2x = 3/2 (divided by two) (x+1)^2 = 5/2 (completed the square & added one to both sides) (x+1)^2 - 5/2 = 0 So I put the range was (-5/2, infinity), but the book has...

I'm sorry for this, but what is the range and domain of the following function? y = 24 - 2x y has to be positive (y > 0) and x too (x > 0) How would you solve this? Do you just need a look and then be able to write it down? Or do you need to solve it with algebra? I've found that x can only...

Hi, I've attempted these problems since Sunday morning but I'm still stuck! Please help... These are not homework problems but these are some problems that I'm working on over the summer by myself. Homework Statement 1. Let I_1, I_2,... be ideals in an integral domain. a. If I_1...

Hey here is the question has a few parts to it. Let f(x)= (x-1)^1/2 and g(x)= 2x^2/x^2+1 a) State the domain and range of f using interval notation. b) State the domain and range of g using interval notation. (Hint: At x=0, g is 0. For x(cannot=0) it helps to write g(x)=2/1+1/x^2 and...

Homework Statement If F is a field than does it imply it must also be a Euclidean domain?The Attempt at a Solution Yes since for any a,b in F. a=bq for some q in R. In fact let q=(b^-1)a. So the remainder which occurs in a ED is always 0. So the rule for being a ED is satisfied in any field.

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1. Problem Statement Write time-domain expression for electric field e(r,t) of unifrom plane wave with amplitude Eo and frequency f= 1 GHz propagating in free space. The plane wave is propagating in yz plane, 30 degrees from the +y-axis, and 60 degress from -z axis. It is linearly polarized...

Homework Statement If A is a subring of B and B is in a particular domain like a UFD than does it imply A is also in that domain B lives in hence also a UFD?The Attempt at a Solution Z is a ring but not a field. However Z mod p is a field. And Z mod p is a subring of Z. Although Z mod p is a...

Say I define a function f by sending a well ordered set X to the least element in X. For example, if N is the natural numbers with the usual ordering, then f(N)=1. This function seems to be well defined. I guess its domain is the set of well ordered sets, but this sounds strange. Whats even...

Aaah! - sin(wt) - time or frequency domain?! hi guys going a bit blank now... been thinking a bit too much about time and frequency domain to a point where I've confused myself a bit... The well known function: f(t) = sin(wt) It is evident that this expression is in the time...

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Just a quick question which came to my mind when reading a historical article on Newtons second law. Is \overrightarrow{F}=\frac{d\overrightarrow{p}}{dt} correct in the relativistic domain because the mass is not necessarily constant?

Ok, f(x)=x^2 g(x)=sq.rt.(2-x) Problem: f(g(x)) You end up with the answer 2-x but how come you need a domain for the answer? How come the domain is (-infinity,2]?

suppose x is a real variable. what is the domain of the function \sqrt{{x-3}\over{x-1}}? here {{x-3} \over {x-1}} \geq 0 from this we get the domain to be \left(-\infty, 1\right) \cup \left[3, \infty\right) but if we write the function \sqrt{{x-3}\over{x-1}} =...

Ok, i think i understand this one, but it's giving me a bit of trouble in terms of comprehension, so I thought I'd get some help on it. I need to find and sketch the domain for: f(x,y)= \frac{x^2 + y^3}{x^2 + y^2 -1} The way i see it, that would only be undefined when the denominator...

Hi everyone, After recently moving from my workplace to work remotely using a laptop back in blighty, I found my work-borrowed laptop is part of a network domain. This prevents me from using the network wizard to setup a new connection to the internet through my wireless network at home...

okay i have three limits, i did one and the two others i m stuck... well here 1. limit when x tends to zero of (x-sin(px)) / (x-sin(qx)) p and q are positive integers. for this one i have no idea what to do, i never worked with p or q... 2. limit when x tends to zero of the function...

Hello everyone! I was wondering if someone could check to see if i did this problem correctly. THe directions are the following: Fid the truth set of each predicate. predicate: 1 <= x^2 <= 4, domain: Z. Where Z stands for integers and <= stands for less than or equal to. The book did...

If f(t) = sqrt(t2 - 16), find all values of t for which f(t) is a real number. Solve f(t) = 3. All right, I know that I have to find values of t that would make the expression under the radical negative. I was trying to set up an equation to just get the domain. t2 - 16 > 0 this would...

Can the domain of f'(x) be larger than the domain of f(x)? Here's my work, as per the rules:smile: The problem I'm working on states f(x) = x + √x and says to find f'(x), the domain of f(x), and the domain of f'(x). I found that f'(x)=1, so I want to say that its domain is all real...

I am doing a bit of complex analysis and there is a definition: An open connected subset of C is called a domain. Why do they choose open instead of closed? Why not include a closed connected subset of C be a domain also?

I'm confused on this domain question 10/ln x I really don't know where to start. Do I graph it and then go from there? :confused:

Here is the problem again x^2-6x+9 / x^2 I think the answer is "all real numbers", but I don't know. I'm not used to seeing only x^2. Most of the ones I have done are x^2 - 4 or something like that.

Please can anybody help me on this two functions it confuse me because has two and thee variables. Find the Domain and Range of each of the following functions a)f(x,x)=\sqrt{\frac{x-y}{x+y}} b)f(x,y)=\[in{(x^2+y^2+z^2)}

Any explanation would be great. Also, are there any examples of finite Integral domains that aren't fields?

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I have a homework problem that goes something like this: There's a circuit, A capacitor in parallel with a resistor, and those two are in series with another resistor. The values of the resistors are given, but the capacitor's is not. Then its given that Z(s) of the circuit equals some...

Please Help! Let f be the function given by f(x)=2x/sqrt(x^2+x+1) a)Find the domain for f. Justify your answer. b)Write an equation for each horizontal asymptote of the graph f. c)Find the range of f. Use f'(x) to justify your answer. Note: f'(x)=(x+2)/(x^2 +x+1)^.5 Please help...

I have this inequality: 4x^2 - 160x + 1500 \le 900 I brought the 900 to the LHS and found the roots (35.81, 4.19). Now I just need the domain of integral values that satisfy. Can I say 5 \le x \le 35?

The switch in the following circuit has been close for a long time and is opened at t = 0. Transform the circuit into the s doman and solve for Isubl(s) and Isubl(t) in symbolic form. I've only found Isubl(s) so far, and I want to see how I'm doing before I convert it back to the time...

It can be said that whatever is outside the observational domain of scientists is outside the observational domain of science itself. How can it then be supported at all that historical entities can be shown to exist using science? Of course, a historical entity which exists to this day can of...

What does it mean to have something in the "public domain" Someone noted in another thread that when something is printed in the newspaper, it is free to use by all and is in the public domain. Obviously this isn't true but i was wondering what is the legal requirements for something to be...