Recent content by psycho2499

This is the part that confuses me. Should I be saying something to the effect: For any a\inA there exists a unique b\inB and a unique c\inC such that f(a)=b and g(b)=c. It follows that g(f(a))=c. Thus (g o f)^(-1)(c)=a

"Since c is arbitrary, it suffices to prove that (g∘f)−1(c)=a as well. How can you do that?" I don't quiet understand your question, or the statement before it.

Homework Statement Let f:A->B and g:B->C be invertible mappings. Show (g o f)^-1 = f^-1 o g^-1. Homework Equations A mapping is invertible iff it is bijective The Attempt at a Solution I understand why these are equivalent statements; however, I can't figure out the wording of the...

Yeah I guess that would work since things are equivalent if they are a bijection. Thanks man

Homework Statement Prove the pigeonhole principle directly. so basically |Nk-{x}|=|Nk-1| if k>1 is an integer and x belongs to the set of naturals. Homework Equations The Attempt at a Solution I have no idea even where to begin.

this is what i get for only half paying attention to what i type. damn finals. 2^k, Sorry bout that

sorry i meant to say 2^n for the eq.

I can never remember how to expand a summation into form: \sumnk=1(22). Thats just a recent example. I can't remember the expansion form any sort of summation really except when it has a defined upper bound.

It would be the chain rule but in tandum with the product rule which I forgot to do anyway, and thank you for catching that.

The extracts of different plants.

If say cold butane bound to something ( butane as a solvent ) is poured into warm water, then what happens. I don't believe anything will happen except the butane will boil off and what is in the solution will fall off to the bottom till the water is cooled completely but I'm just checkin with...

Sorry this took so long. Originally I was looking at how you did it not the question and what the answer should be. You forgot a negative from d/dx(1/x) but I'm pretty sure you can't do it that way. As far as I know you can approach this straight on or using a ln trick. I'll show both...

My teacher used to say that the easiest way to remember sin theta is Y sin

The definition of sin theta in any case is opposite/hypotenuse and cos theta is adjecent/hypotenuse. The unit circle has a radius of 1 so any right triangle with vertices at the origin, a point P on the circle, and the X or Y axis ( is a purely your choice, most choose the X axis ) will have a...

Well the only mistake I see in your first work is that you forgot a negative. and for the second problem break it down to a more simple problem. It may become more work to resimplify it later but you aren't wrong to do so. You can take it and make it into this d/dx((x-1)(1/2)/(x2(x-4))(1/2))...