Domain Definition and 743 Threads

Homework Statement Graph x^(1/3) +x^(4/3) Homework Equations Limits, derivatives, etc. The Attempt at a Solution Hi guys, I was attempting this problem and then verifying it using a function grapher online. I noticed that all of the function graphers do not plot the function...

Homework Statement I know that this prob isn't calc, but I'm learning it in calc class now so i thought it would go here :) Anyways, these 3 functions y=1/(x2 y=(x+4)-2 y=1/(x2-x-2) The Attempt at a Solution for this, y=1/(x2 the domain is (-infinity,0)U(0,infinity)...

Homework Statement Prove that R is a PID (principal ideal domain) when R is a ring such that Z \subset R \subset Q (Z=integers, Q=rationals) Homework Equations The Attempt at a Solution So I'm not really sure how to start this problem. I know that a principal ideal domain is an...

hi ... i want to ask about domain theory of ferromagnetism... first of all , According to classical electromagnetism, two nearby magnetic dipoles will tend to align in opposite directions, so their magnetic fields will oppose one another and cancel out. how does this happen? after this ...

The Question is: What is the Domain of the function f(x)= log_{5}(log_{5}(x + 2) My answer is that the Domain is (-2, \infty). However the it is said that the right answer is (-1, \infty) and I am not convinced so can anyone give me an explanation?

Hi, I ran into conflicting definitions of integral domain. Herstein defines a ring where existence of unity for multiplication is NOT assumed. His definition of integral domain is: "A commutative ring R is an integral domain if ab=0 in R implies a=0 or b=0" I looked in 3 other books and...

Homework Statement let f(x) = sqrt(1-sin(x)) Homework Equations What is the domain of f? What is the domain of f'(x)? The Attempt at a Solution I understand that the domain of f is all real numbers not including every increment of 90 degrees, but I am not sure how to state that...

Hi together ... I encountered the following statement: Operator A is self adjoint on D(A) then A(t) \equiv \exp(iHt) A \exp(-iHt) is self adjoint on D(A(t)) \equiv \exp(-iHt) D(A). H is self adjoint, so that exp(...) is a unitary transformation. But why does the domain transform this way...

messing around with a function changes it's domain?? consider a function f(x)= \sqrt[3]{2x^2-x^3} if i take x^3 common from inside the cube root the function becomes f(x)= x*\sqrt[3]{2/x-1} the domain of the orginal function includes all real numbers, but the domain of the "new" function...

1) Find a continuous function f: (0,1)->R with f[(0,1)]=R I couldn't think of any function except tangent, but its domain is NOT (0,1) though? Any suggestions? 2) Find a continuous function f: (0,1)->R with f[(0,1)]=[0,1] I couldn't think of any function that I know. Any suggestions? 3) Find a...

I'm trying to figure out what faraday's law is in terms of frequency rather than time. I think the equation is V = -N*B*A*2f. Where N is the number of turns in the loop, B is the magnetic field, A is the area and f is the frequency. However I am not totally convinced that my derivation is correct.

Homework Statement Prove that if we have two commutative rings R and S and form the product R X S, then R X S cannot be an integral domain. The Attempt at a Solution We have that an integral domain is a commutative ring with 1 not= 0 and with non-zero zero-divisors. ==> (1,0)X(0,1)...

Homework Statement I'm working with a heat equation that requires a Laplace transform. I performed the transform and ended up with a basic ODE with a particular solution. I solved for the particular solution and then realized I was working on an infinite domain in my spatial dimension...

Homework Statement Suppose R is an integral domain. Suppose c in R has c^2 = 1. Prove that b must equal either 1 or -1. Also, in Z/12Z, find an element b not equal to -1 or 1, with b^2 = 1 The Attempt at a Solution So for the first part, I'm guessing it would be a good idea to factor...

Homework Statement Find the domain and the range f(x,y)=2x2+3x2+1 Homework Equations non The Attempt at a Solution ... i said that x,y are all real #'s and f(x,y)>=1 or z>=1 is there anything wrong with what i has attempted at? if do could you explain... thanks in advance

The Problem Hi, I am trying to modulate two sinusoids in Matlab. I have some and some , where fx and fc are different frequencies. I then modulate them together, using dot multiplication, . I then plot each in the time domain using and I obtained the correct solution. The problem comes with...

can anyone explain that domain or give me any reference about it??

Hey guys, I am totally lost in the idea why we have to change function in time domain to frequency domain to ease with our calculations. Let me break my question into serveral smaller ones. 1)What is the physical implication of transferring a signal to frequency domain? (I know that in...

Could someone please explain to me what the range and domain of a function is and how to find them? I just don't understand what they mean Thank You

I was thinking how do I differentiate the domain of functions... Suppose I have a function: f(x) = \left\{\begin{matrix} x^2 -1, \;\; |x| \leq 1\\ 1 - x^2, \;\; |x| > 1 \end{matrix}\right. And I need to derive it: f'(x) = \left\{\begin{matrix} 2x, \;\; |x| \leq 1\\ -2x...

Homework Statement Given f:A→B and g:B→C, let h=g(f(a)) If h is injective, then g is injective. Give a counter example. Homework Equations Injection: Let f:A→B For all f(x1)=f(x2) implies x1=x2 The Attempt at a Solution f(a)=\sqrt{a} from [0, infinity]→[0,infinity]...

So I'm skipping pre-cal with full intentions of picking up on AP Calc. Our summer course work is taken from a book called preparing for calculus. After giving me some who-dad that I knew already everything changed in an instant. There's a little gap that isn't quiet filled. A function is...

Hello! I'm not quite sure where to put this. I'm programming, but my question should be strictly mathematical. However, just for your information, I'm programming with Mathematica. I have a function that will give me points. If I give it inputs, I can get a value out of it. I can take a...

Homework Statement Let f(x)=e^(-x)-x ,, x belongs to R Find the domain of f inverse Homework Equations Domain of f inverse = range of f The Attempt at a Solution we have : -inf < x < inf -inf < -x < inf ... (1) 0 < e^(-x) < inf ... (2) By adding (1) and (2) ...

Homework Statement a) Show that $\sum_{S(j)} a_j + \sum_{R(j)} a_j = \sum_{S(j) and R(j)} a_j + \sum_{S(j) or R(j)} a_j$ is valid for an arbitrary infinite series, provided that 3 out of 4 sums exist. b) Show that $\sum_{R(j)} a_j = \sum_{R(c-j)} a_{c-j} for an arbitrary infinite series where...

In algebra/trig. what kinds of problems have a domain and a range ? Is this true for anything that can be graphed? Because a lot of the time after you finish a problem in precalc. it then asks for the domain or range, so the question becomes, in mathematics, is it possible to find the domain...

If the domain of a function is countable, then is its range also countable? also if A is countable and B is countable is A(cartersian product)B countable?

Homework Statement I am given an LTI system where I need to obtain the impulse response and difference equation of H(z). H(z) = (1-0.5z^-3) / [(1-0.5z^-1)(1-0.25z^-1)] and |z| > 0.5 Homework Equations The Attempt at a Solution I am pretty lost about what to do. I...

how is euler's formula useful? it must have something to do with converting from the time domain to the phasor domain and back, but i can do that without euler's formula

"Natural Laws" and their domain of validity What is the philosophical justification for extending observed phenomena to "laws of nature". For example, Galileo dropped massive objects and saw that they fall at the same rate, but to then say that all massive objects fall at the same rate requires...

\int _1 ^e \int _{1/e} ^{1/y} f dx dy If asked how to sketch the bounds for that: "x starts at x=1/e and ends at x=1/y 1/e is just a constant so that's a straight line and x=1/y is the exact same line as y=1/x" That's a decent enough engineer's explanation right? (no one in university should...

Homework Statement For f(x)=((x^(2)-2x-3)/(x-3)), restrict the domain of f(find Dom (f) first) so that Rnage(f)=(-2,4)U(4,11) The Attempt at a Solution I found that when x=3, the function will be undefined. so the domain(f) should be (-infinity,3)U(3,+infinity). I GUESS now I should go...

Prove that the solution of the CP y'=-(x+1)y^2+x y(-1)=1 is globally defined on all of \mathbb{R} How would you go about this? I thought about studying the sign of the right member if the equation. But what would I do next?

Please give geometrical desciption of what are characterstic curves and domain of dependence of a PDE. Please help. Thanks.

Homework Statement Given two functions f(x)=\frac{x}{x+1} , g(x)=\frac{x+2}{x} (1) find the domain of f and g so D_f all real x , x\neq -1 D_g is all real x , x\neq 0 (2) Find the composite function gf and state its domain and range g o f = 3+ 2/x , then its domain would...

I read a lot of books on the uniqueness theorem of Poisson equation,but all of them are confined to a bounded domain \Omega ,i.e. "Dirichlet boundary condition: \varphi is well defined at all of the boundary surfaces. Neumann boundary condition: \nabla\varphiis well defined at all of the...

hi ,,,, Homework Statement these are the function 1) f(x)=A(x)/B(x) 2) f(x)=√(A(x)) 3) f(x)=√(A(x))/(B(x)) 4) f(x)=(A(x))/√(B(x)) 5) f(x)=√(A(x))/√(B(x)) 6) f(x)=√((A(x))/(B(x))) The Attempt at a Solution the domain are they right 1) { x∈ R : B(x) ≠ 0 } 2)...

Homework Statement δu/δt+2tδu/δx=1 for t>0,x>0 with u= 0 on x= 0 for t>0, u=1 at t=0 for x≥0 Homework Equations The Attempt at a Solution ((dx)/(dt))=2t x=t²+c x-t²=c the general solution is: u=t+F(x-t²) Now i am...

Homework Statement Let the function f: [1,infinity)-->R f(x)=\left\{ \begin{array}{rcl} \frac{(\sqrt{x}-1+x\sqrt{x-1}}{\sqrt{x^2-1}} & \mbox{,} & x>1 \\ c, x=1 \end{array}\right. Find the EXACT value of c for which f is continuous on its domain. Homework Equations N/A...

Just wondering how to write the domain of where a function similar to this is continuous: using proper domain notation.

1.Let R be a ring such that Z ⊂ R ⊂ Q. Show that R is a principal ideal domain. We show that Z is a principal ideal domain, so every ideal in Z which is also in R is principal. But I'm not sure how to use that R is contained in Q. 2. Proof that X^4+1 is reducible in Z/pZ [X] for every...

Homework Statement S = { z | |Im(z)| < 5 }, z is a complex number Homework Equations I am trying to generate a mobius transformation w = f(z) such that it will map S onto a unit disc but I keep running into problems and contradictions. I think there is a big mistake in my attempt but I...

I came across this weird graph from another thread: y=\left(x^2-6x+8+\sqrt{x^4-12x^3+52x^2-96x+64}\right)^2 It seems that there is a root y=0 for the domain x=[2,4]. I've never seen such weird behaviour on a graph before. How could analysis of this function (or not?) determine that there...

Hi, I'm working on a calculation of flow through a rectangular duct and I'm assuming I'm in the Stokes' flow regime (Re<<1), but I also want to experiment on this system and I was wondering if anyone knows until what Re-number Stokes' flow is still a good approximation (and how good, i.e. in...

Symmetry breaking "domain walls" The only "spontaneously broken symmetry" that I can easily visualize, is cooling down a ferromagnetic material and having the spins randomly choose a direction to align. Since the choice is random, different regions will usually choose different directions...

I was working on the following problem from a textbook. The textbook has no answer. I have included my solution - I am not sure whether it is correct Any ideas and or solutions? (guidance) Question: Suppose that f is any function with domain (-infinity, +infinity) a) Does the function g...

Homework Statement I am trying to find the domain of the following.. R^2 to R^3 of g(x,y) = (x-y,x+y,3*x) R^3 to R of h(x,y,z) = x/(y+z) Homework Equations The Attempt at a Solution I don't know how to start. I know how to find the domain in one dimension but how...

Homework Statement Find the range for the function; fg(x) and state its range where f(x)= e^{2x} + 3 and g(x) = ln(x-1) The Attempt at a Solution Putting g into f I reach; fg(x) = e^{2ln(x-1)}+3 (1) - here is where I have the problem, now, I know that it simplifies down to fg(x)...

Homework Statement Find the domain of the function. h(x) = \sqrt{4 - x} + \sqrt{x^2 - 1} Homework Equations a2 - b2 = (a - b) (a + b) I think that's all... The Attempt at a Solution For starters, I know we can't have a negative number in the radical. I looked at the 2nd radical first and...

Hello. I am watching this video: https://www.youtube.com/watch?v=xIQtnQ9XPbE and he says there: I see that the wave turns into a "normal" sinus in the end, but it's not constant. I think, that even on an unmatched transmission line, the waves should go back and forth, but eventually...