Composition Definition and 388 Threads

1. Show that the set {f:R-{0,1}\rightarrow [b]R-{0,1}}, of functions under composition, is isomorphic to S _{3} f_{1} = x f_{2} = 1 - x f_{3} = \frac {1}{x} f_{4} = 1 - \frac {1}{x} f_{5} = \frac {1}{1 - x} f_{6} = \frac {x}{x - 1} Homework Equations The Attempt at a Solution...

I have a homework problem as follows: Let f(x) = 2x, (-inf < x < inf). Can you think of functions g and h which satisfy the two equations g \circ f = 2gh and h \circ f = h^2 - g^2? I know that g \circ f = g(f(x)), which then = g(2x) for the first question. I can't figure out how to work...

Homework Statement Let A,B be sets and let f:A \rightarrow B and g,h:B \rightarrow A be functions. (1) Suppose h o f is an injective map from A to itself. Show that f is injective. (2) Suppose now that f o g = 1_{B} and hof = 1_{A}. Show that f is bijective and g=h. P.S. given that f...

My daughter, Evo Child, is a university student and an English tutor, (her university pays her to tutor other students). She's been tutoring since High School (honors English). She asked me if I thought anyone at PF would be interested in having help with their English. She will be glad to...

A = (0, infinity), B = C = D = R where R is all real numbers f: A->B, g: B->C, h: C->D f(x) = lnx, g(y) = 3y, h(z) = e^z h o g o f ? -------------------------------------------- For the following to be defined doesn't 1) range(f) ⊆ domain(g) 2) range(g o f) ⊆ domain(h) So g o f should be...

For the following to be defined doesn't 1) range(f) ⊆ domain(g) 2) range(g) ⊆ domain(h) Is that correct? So R ⊆ R for 1, and R ⊆ R for the other so it is ok? --- Second question: but how can you have the function h with the range of all real numbers when the exponential function only has a...

This website gives a break down of the ten most abundant elements from spectrum analysis of the sun http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961112a.html" Presumably this result is only valid for the surface/near surface of the sun. If there were any heavier elements present...

Homework Statement You are given a sample of cinnamon oil with some kerosene oil dissolved in it.Propose a method to determine atleast approximately the percentage of kerosene oil present in this sample,by volume. N.B. 1) you are provided with facilities for various types of distillation 2)...

Homework Statement An herbicide is found to contain only C, H, N, and Cl. The complete combustion of a 100.0-mg sample of the herbicide in excess oxygen produces 83.16 mL of CO2 and 73.30 mL of H2O vapor at STP. A separate analysis shows that the sample also contains 16.44 mg of Cl...

Homework Statement A = {0, 1, 2, 3} f and g are functions mapping A to A where f = {(0,1),(1,2),(2,0),(3,3)} and g = {(0,2),(1,3),(2,0),(3,1)} find (f o g)(1) Homework Equations The Attempt at a Solution The answer is 3 but i can not get it.. the (1) on the right side...

Homework Statement I am running an experiment in which I have a compound of SiO2 Na2 K2O PbO I am trying to figure out the percent composition of oxygen given that the percent composition of the compound is: 46% SiO2 5% Na2 4% K2O and 45% PbO Homework Equations 46% SiO2 5% Na2 4% K2O and...

I have been able to find lots of information about experiments that have been done to determine how different compositions of matter respond in a gravitaional field. However, I have not been able to find any information about experiments done to determine any difference in strength of the...

Hello, Given (in spherical coordinates) the resulting 4-vector K of the composition of 2 Lorentz pure rotations R1 and R2, where only R1 is known, I would like to find the angle of the "overall" rotation resulting from this composition. In other words, I want to find the symbolic expression...

Theorem 2.15: Let A be an m x n matrix with entries from F. Then the left-multiplication transformation L_A: F^n --> F^m. Furthermore, if B is any other m x n matrix ( with entries from F ) and B and D are the standard ordered bases for F^n and F^m, respectively, then we have the following...

Homework Statement I've been looking at how integrable functions behave under composition, and I know that if f and g are integrable, f(g(x)) is not necessarily integrable, but it -is- necessarily integrable if f is continuous, regardless of whether g is. So I was wondering, what about if g is...

Theorem 2.12: Let A be an mxn matrix, B and C be nxp matrices, and D and E b qxm matrices. Then (d.) If V is an n-dimensional vector space with an ordered basis B, then [IV]B = In. My question: What does [IV]B mean? Is this the identity matrix with respect to the vector space V which is...

I am reading (theorem 2.14) from a textbook, and don't understand how g = Tf and (#1) line of reasoning. The theorem and proof is as follows: Theorem 2.14: Let V and W be finite-dimensional vector spaces having ordered bases B and C, respectively, and let T: V-->W be linear. Then, for...

Hi, Homework Statement Given: f(x)=x^2+2 and g (x)=\sqrt{x} Find: f \circ g and g \circ f 2. The attempt at a solution f \circ g =f(g(x))=x+2 , where x\in (-\infty ; +\infty) g \circ f =g(f(x))=\sqrt{x^2+2} where x\in (-\infty ;+ \infty) I haven't done this for a...

Homework Statement Let a=fx+g and b=hx+i. For which real numbers f,g,h,i a∘ b = b∘ a Homework Equations The Attempt at a Solution a∘ b(x)=(a(b(x))= h(fx+g)+i= fhx+gh+i b∘ a(x)=(b(a(x))= f(hx+i)+g= fhx+fi+g I'm kind of stuck here as I don't think I know what the question is...

A metal alloy consists of magnesium and aluminum.When a 1.00g sample of the alloy is reacted with excess HCl, 0.0989g of hydrogen gas forms. Calculate the percent composition of the alloy. Ok I got the following balanced equations : Mg + 2HCl -> MgCl2 + H2 2Al + 6Hcl -> 2AlCl3 + 3H2...

This might be a silly question: given a function g is it possible to find a function f such that f = f \circ g?

Hi, given two functions f and g, is there any known condition under which the following is valid: (f \circ g^{-1}) = (f^{-1} \circ g) Basically I have to find out the requirements for f and g for which composition is commutative in respect to inversion.

Homework Statement A rigid cylinder of 1000cm cubed contains 4.168grams of an ideal gas mixture. The gas mixture consists of methane and ethane at a temperature of 100C and a pressure of 500kPa a) Estimate the average molar mass of the mixure b) Calculate the composition of the mixture on a...

Homework Statement Here's the question form the text. (I have the answer, but don't know how to do part c. "A solution contains 50.0g of heptane (C7H16) and 50.0g of octane (C8H18) at 25 C. the vapor pressures of pure heptane and pure octane at 25 C are 45.8 torr and 10.9 torr...

Homework Statement Consider the map F: C0([a,b],Rn) --> R, F(\phi)=\int\phi(t)\phi(t)dt (This is the integral from a to b). Write F as a composition of three maps, each of which is linear or bilinear. Then use the chain rule and generalized product rule to compute DF(\phi). Homework...

Homework Statement Calculate and tabulate the fractions of the total mass of the Earth which would be accounted for by O, Na, Mg, Al, Si, S, Ca and Fe under the following hypothese. i) All the elements above are fully oxidized, except that no S is accreted and the Fe is entirely metallic...

Homework Statement I am given a table with the abundances of atoms of different elements per 1000 Si atoms. The question wants me to tabulate the fraction of mass of the Earth that each element, and different oxides contribute. But to do this I need to know how many Si atoms there are so I...

Homework Statement A 5.00g sample of natural gas, containing methane, CH4, and ethylene, C2H4, was burned in excess oxygen, yielding 14.5g CO2 and some H2O as products. What percent of the sample was ethylene? Homework Equations Moles and percent composition The Attempt at a...

Homework Statement F o G(x) F(x)=1/x+1 g(x)=2x-x/x+3 Simplify Homework Equations F o G=f(g(x)) The Attempt at a Solution Here is the order of things I did. F(2x-1/x+3) to 1/(2x-1/x+3)+1 Ok, this sounds stupid but, I can solve these, but when I get stuff like this that has...

Homework Statement a.) F = {(1, a), (2, b), (3, a), (4, c)} G = {(b, 1), (a, 2), (c, 3)} i. Find F o G ii. Find G o F b.) A function F: N x N --> N is represented 2(m + n) + 1 for F(m, n) i. Is F one-to-one? ii. Is F onto? c.) Prove by Mathematical Induction...

Homework Statement Describe the composition and temperature of the equilibrium mixture after 1.0 kg of ice at -40*C is added to 1.0 kg of water at 5.0*C.Homework Equations \begin{gathered} Q = mc\Delta T \hfill \\ Q = mL \hfill \\ \end{gathered} Book answer:1.2kg ice, 0.80 kg water...

Homework Statement This is from Advanced Physics by Adams and Alday, section 9.11, question 2 c. What is the quark content of [snip] Λ baryon, strangeness = -1, mass 1.12 GeV/c2? Homework Equations No equations. Table of masses at http://en.wikipedia.org/wiki/List_of_particles. Strangeness...

Homework Statement Find the function g(x), if there are h=g \circ f f(x)=x+1, x \in \mathbb{R} and h(x)=x^3+3x+1 Homework Equations (g \circ f)(x)=g(f(x))=h(x) f \circ g \neq g \circ f The Attempt at a Solution h=g \circ f h(x)=g(f(x)) x^3+3x+1=g(x+1) Is there any...

Whats the chemical composition of oak wood? I want to know because I am trying to cut wood by changing the chemical compound of the places that i want to cut it at by putting a chemical that would bond to the wood, and the new compund of my chemical and wood would be a gas. I don't know if...

what is the composition of black hole? is it a matter or antimatter or energy?

Homework Statement Initially a mixture contains 0.723 mol each of N2 and O2 in an 7.20 L vessel. Find the composition of the mixture when equilibrium is reached at 3900°C. For the reaction below, the Kc = 0.0123 at 3900°C. N2(g) + O2(g) 2 NO(g) Homework Equations I.C.E Tables (not...

how do i take the derivative of sqr(4 + sqr(3x))? My teacher wants me to do it as a chain rule composition function so i separated it into F(x)= (4+x)^1/2 and G(x)= (3x)^1/2 but i don't know where to go from here because i don't know how to take the derivative of f(x)

1. For a problem I require the atomic density of uranium atoms per cm^3 in a solution of water. The atomic fraction of natural uranium to water is 1 per 100 and the net density of the solution is 1 g/cm^3. (Natural uranium is assumed to be U-235 at 0.72% of uranium atoms and the rest is U-238)...

In Micheal C. Gemignani, "Elementary Topology" in section 1.1 there is the following exercise 2) i) If f:S \rightarrow T and G: T \rightarrow W , then (g \circ f)^{-1}(A) = f^{-1}(g^{-1}(A)) for any A \subset W . I think the above is only true if A is in the image of g yet the book says...

Homework Statement If you invest x dollars at 4% interest compounded annually, then the amount A(x) = 1.04x. Find A o A, A o A o A, and A o A o A o A. What do these compositions represent? Find a formula for the composition of n copies of A. Homework Equations f o g = f(g(x)) The...

Homework Statement Prove that if f: G \to H and g: H \to K are homomorphisms, then so is g \circ f: G \to K. 2. The attempt at a solution Since f is a homomorphism (G, * ) and (H, \circ) are groups and f(a*b)= f(a) \circ f(b), \forall a,b \in G. Likewise, (K, +) is a group and g(f(a)...

What is ...Dust? I know this is quite ackward and may not be the right place to ask such a question but I am a bit curious to know something good about it: Earth is composed of soil; Soil is a mixture of elements and compounds; But we don't use the soil around us to extract those compounds...

In regards to two types of engines.. What gases (by percentage) are to be found in conventional petrol driven internal combustion engines, such as found in cars ? What gases (by percentage) are to be found in conventioanl diesel driven internal combustion engines, such as found in trucks ...

[SOLVED] pH question... i'm writing a research paper on the organic medicinal massage oils. i need to know the chemical composition of citric acid and it's pH. can anyone help me?

when you have .283 moles of water and .503 moles of copper sulfate, how do you find the mole ratio between the water and coopper sulfate?

I need to determine the quark composition of the neutral antikaon. Below is a copy of my multiple choice question. http://img166.imageshack.us/img166/2025/quarksec1.jpg Here is my attempt at a solution: First, a neutral antikaon is a meson. This means it must be composed of a...

Homework Statement The superposition of two waves, [see attachment - it doesn't let me link the attachment because I'm new ;P] at the location x = 0 in space results in what kind of wave behavior? [As in, how often does it beat and what frequency is the sound?] Homework Equations Wave...

I understand that most scientists believe that the Earth's core is composed of iron, nickel and perhaps some other elements such as sulfur and oxygen. I also understand that they believe that the Earth's core formed during a time when the Earth was molten and that the core was formed by heavier...

Homework Statement Prove or give a counterexample: the product of any two self-adjoint operators on a finite-dimensional inner-product space is self-adjoint.Homework Equations The only two equations I've used so far are: \left\langle T v, w\right\rangle = \left\langle v, T^{*}w\right\rangle and...

Homework Statement The densities (at 25*C) of tin and lead are 7.3 g/cm3 and 11.3 g/cm3 respectively. Plumber's solder is an alloy of tin and lead and has a density of 9.7 g/cm3. Estimate the composition by mass, of the two metals in this solder. Homework Equations The Attempt...