Domain Definition and 704 Threads

So just had this question as extra credit on a final: Let D be an integral domain, and suppose f is a non-constant map from D to the non-negative integers, with f(xy) = f(x)f(y). Show that if a has an inverse in D, f(a) = 1. Couldn't figure it out in time. I was thinking the way to go...

if a function f is differentiable of [0,2pi] can I integrate its derivative df on [-pi, pi]?

Homework Statement Find the Fourier transform of the following signal JUST by using the FT table and the FT properties x(t) = sin(t) -pi<=t<=pi 0 otherwise NOTE: I am using CONVOLVED WITH as a substitute for * (the real convolution operator) because I cannot express...

Hey guys, Does anyone know of a good, free domain coloring grapher? I can't find a decent one anywhere.

Let R be an integral domain. Then R is a PID if the following 2 conditions hold: 1) any 2 elements a, b \in R have a greatest common divisor which can be written as ra + sb for some r, s \in R . 2) If a_1, a_2, ... are nonzero elements of R such that a_{i+1}|a_i for all i, then there is...

I was wondering if there is an easier way to solve circuits using matrix inversion if I have complex numbers. So far I've been doing them by hand with 2x2 matrices. It isn't hard, but it takes a while. I have a test coming up in about a week which will have 10 questions that have to be solved in...

Check this out: \int_{-1}^{0} ln(x) dx u=ln(x), dv=dx du=\frac{1}{x},v=x \int_{-1}^{0} ln(x) dx= x\space ln(x) \|_{-1}^{0} -\int_{-1}^{0} \frac{x}{x} dx =x\space ln(x) \|_{-1}^{0}-x \|_{-1}^{0} =\lim_{x\to0} x\space ln(x)-(-ln(-1))-(0-(-1)) \lim_{x\to0} x\space ln(x)=lim_{x\to0}...

I'm having an interpretation problem with the notation used in physics, under the integration sign. What is the proper interpretation of the domain of integration symbol, on the integration sign ? To be more precise, consider a function F(x) of one or several variables. Its integral on a...

Homework Statement when I'm trying to calculate and show the graphic of the phase characteristic i don't understand why the domain range of the arctan function is [0,90] : Homework Equations The Attempt at a Solution shouldn't be the domain of arctan function between...

Find the domain of the function f(x)= (3x+5)1/2. Not quite sure how to even start this...

Homework Statement Consider some simple single-variable function such as f(x)=2x+1 The domain,codomain and range of the above function is set of all real numbers. But why not the set of all complex numbers? if x = 3+4i f(x) = 6+8i + 1 = 7+8i,so it is possible for x to be a complex no...

Homework Statement Determine the domain and range of the function y=5−e^(−x/2). I am having some trouble with this. Does any have some tips to get started, or a good link to a instructional video? My textbook does not have this section :( Thanks all! Homework Equations The...

Hi All, I'm just trying to practice graphing signals in frequency domain and I came across a stiuation I wasn't familiar with. If the exp() has a constant*t in it I'm not sure how to graph it, I remember that just cos it like a double sided exp(jwt) but with half the magnitude. I've attached a...

Homework Statement What is the domain of f(x,y)=x^y The Attempt at a Solution I thought it would be all real pairs except (0,0) but it is x>0 and y all real numbers?

Homework Statement How to solve part (iv) & (v)Homework Equations general form : y = a(x-h)^2 + kThe Attempt at a Solution In part (iv) for finding domain and range I converted g(x) in general form and then compared it with general form.

Hi all, This question is on the Hilbert transform, particularly on the domain of the input and output functions of the Hilbert transform. Before rising the question, consider the Fourier transform. The input is f(t) and the output is F(\omega). The function f and F are defined over...

Homework Statement If the maximum allowable width, w, of the wall is 100 cm, what are the domain and rand of the function? Remember to include units for both the domain and range. Homework Equations w(d)=2d w(d)=100, so 100=2d, there fore d=100/2 The Attempt at a Solution...

I have a question about domain and range.What are the domain and range of cos(e^{-×}) and \frac{\left|2×-1\right|}{sin(\frac{1}{2}\pi×-\pi)} ?? Thanks..

What must actually be specified in order for a function to be fully defined / or in what combinations if not all 3 need to be specified? I.e - from knowing the function you can determine the co-domain - e.g - if it is specified that real functions are going in, and for something simple like 2x...

I am reviewing for the mathematics GRE subject exam, and I have this review book, and in the book when they speak of the characteristic of a ring they give the following def "Let R be a ring. The smallest positive integer n such that na = 0 for every a in R is called the characteristic of the...

The "correct" domain of self-adjointness for the Laplacian Consider the Hilbert space L^2(\mathbb R^d), and consider the Laplacian operator \Delta on this space. We want to find a domain, D(\Delta) \subset L^2(\mathbb R^d), such that this guy is a self-adjoint operator. We have been talking...

This problem seems a little overwhelming at the point. I am not sure on where and how to start. Suppose that a uniform thermal gradient in the +x direction exists in a very large (i.e. effectively infinite) domain of conductivity $k_2$ such that the temperature field $u_{\infty}(r,\theta)$ can...

Homework Statement I have this function of two variables: f(x,y)=\sqrt{4xy-3y^2} Where I have to declare the domain of the function. Homework Equations Since you cannot take the square root of something negative, when dealing with real numbers. The square root has to be zero or...

Homework Statement Find the derivatives at an arbitrary point x in the domain of the following functions f_i: D_i → ℝ, where for 1 ≤ i ≤ 6 the domain D_i is the maximal subset of ℝ on which the mapping is defined - you don't have to determine the domains. Homework Equations a) f_1 (a) =...

Homework Statement I need to find the domain of sin(arcsin(x)). Now I "know" that this is xε(-1,1), but I don't understand why. If the range of arcsin(x) is (-∏/2,∏/2), then shouldn't this be the domain of sin(arcsin(x))? Help appreciated.

Homework Statement This question here. Can someone please tell me why we have 2 cases to consider. http://archives.math.utk.edu/visual.calculus/0/domain.1/8.html I don't understand why it says we have 2 cases to consider. 8 x - 4 > 0 and x - 3 > 0. 8 x - 4 < 0 and x - 3 < 0...

I need help understanding how frequencies are distributed when taking the FFT of an Image and how can i determine those frequencies, I really need a detailed and easy tutorial with practical example to understand it. When we take the FFT of a Sine/Cos wave we can easily see its frequencies in...

Homework Statement Find domain and range of f(x,y)=\frac{-3y}{x^{2}+y^{2}+1} Homework Equations The Attempt at a Solution It's quite obvious the the domain is R^{2}, because there are no possible values of x or y that would make the denominator 0. But as for the range, my...

As I understand it, there are the terms: domain - variables that are input to a function range - the variable that is output to a function This works well in a canonical single equation system like z = f( x , y ), but breaks down in an implicit function or set of equations. I was...

Hello guys, I need some assistance in calculating the domain of this function: f(x)=ln(sin(pi/x)) I started with sin(pi/x)>0 due to the ln function. From here 0<(pi/x)<pi. That lead me to some calculations giving x>1, but obviously I have periods of 2*pi to include. The answer is: x>1...

I have came up with a solution for this - in order for this function to be defined, we must have an x and y between negative infinity up to and including the number 1. If asked to graph this domain, does the domain lie on the x-y plane of three dimensional space, and is it the intersection of...

Homework Statement Find the domain and range of the following function without the use of a calculator: f(x) = sec (pi x/4) Homework Equations As far as I know, this problem doesn't specifically require "equations". Therefore I am leaving this section blank. Not because I am a...

Homework Statement Ok, I just worked out a composite function, and it left me with: √2x^2+5) Now, how do I find the domain from that? I don't understand that my text says the domain of that is just all Real numbers ? What makes this different than other square functions that we are...

Homework Statement Problem: http://archives.math.utk.edu/visual.calculus/0/domain.1/f6.gif Homework Equations The Attempt at a Solution Look at the pic, and tell me again why I can't do this: http://i47.tinypic.com/bhadsj.jpg

Homework Statement If f(x)=√x and g(x)=√(x^2+1) what is the domain of g(f(x))? The Attempt at a Solution I cam up with (-∞,+∞) since the square root of a square is always positive, am I missing something here?

Homework Statement Here is a picture of the question: Homework Equations The Attempt at a Solution Here it what I did... factored it...so 1 / (x-3)(x+17) domain: (-infinity, -3)(-3,17)(17, +infinity) or rather (-3,17) I know that is not correct. I am really stuck on this one!

What is the domain of f(x)=x^(2/3)? If I take a negative number and square it, the result is positive. For example, (-4)^2 is 16. The cube root is 16 is also a positive number. So I conclude that the domain of this function is "all real numbers". But in Wolfram the answer is "all...

If I am given a function: f(z) = w(x,y) = u(x,y) + iv(x,y) How do I find the domain and range of that function? Are there any good lectures online on this? I know I have to use two planes; One for u and v, and one for x and y. Besides that, I am lost.

I am a bit confused about this matter. While I was studying Calculus I saw an excercise like this: The domain of f(x) [0,2] and the range is [0,1], it also shows its graphic, though it is not important it is something like a parabola, its maximum point is (1,1) and its intersection points are...

Hello, I know the value of a field variable in a 3d mapped finite element mesh. Can anyone suggest an effective method/methods to find its gradient throughout the mesh.

Hello, I have a simple question that has bothered me forever.When I am given a rational function, say, f(x) = (x2+x-6)/(x+3)say I want to look at the domain of this function. Well the first thing that catches my eye is the fact that if I plug in x=-3, the denominator will be 0, which would be...

Homework Statement Hello! Could someone explain some things presented in this example: http://i.imgur.com/wVOxf.png My friend, and I haven't been able to crack it. I get all the x-conditions right, but can't put the whole thing together into a domain. Here it's presented that xe[-2,3] due to...

f(x) = x - 3, g(x) = +\sqrt{x} Q. Find gf(x) and a suitable domain and the corresponding range. so gf(x) = \sqrt{x-3}, f(x) is first and the domain for f(x) is x belongs to ℝ, so the domain for g(x) will be x belongs to ℝ, so this function doesn't work? the answer is the domain is x>=3...

Homework Statement Consider the function f(x) = sin (x) in the interval x ∈ (p/4, 7p/4). The number and location(s) of the local minima of this function are? Homework Equations The Attempt at a Solution I have managed to get one of the minimas (i.e. 3p/2), however i am unsure about...

Preface: I can't understand a solution provided in a textbook. Please help me to understand. Homework Statement Define: f : D_f \rightarrow \mathbb{R} such that f(x) = \sqrt{x+2} and Domain(f):=D_f = \{x \in \mathbb{R} : x \geq -2\} Find the range of f(x). 2. The textbook's solution...

Homework Statement Find the domain and range of the function: F(x) = \frac{x}{lxl} Homework Equations ? The Attempt at a Solution domain is all x such that x ≠0 range: do i have to make this into a piecewise function, if so, how?

How will the graph of a sine wave (plotted against time axis) of a particular frequency look like if the same is plotted against frequency?

Homework Statement Eliminate the parameter to find the Cartesian equation of the curve. Problem #1: x = sin t, y = csc t, 0 < t < ∏ / 2 Problem #2: x = sin θ, y = cos 2θ Homework Equations What's shown above is what's listed in the book. However, the authors felt compelled to...

It's a pretty basic equation: x = x^u, solve for u. ln x = u ln x ln x / ln x = u u = 1 However, this solution only applies for x > 0. Is there any way we could solve this equation for all values of x?

Homework Statement Let R be an integral domain. Say a prime p \in R is small if a\in\bigcap\limits _{n=1}^{\infty}\left\langle p^{n}\right\rangle = \left\langle 0\right\rangle Show that if p is a small prime and D = R \setminus \left\langle p\right\rangle then R_D is a principal ideal...