in database we study the fisibility \njust tell me who does this function works \nand is is ment by (rate, range) for me i c it's xy-coordenets
216810
Rate is the discount rate over a period.\nThe range is probably the list of values representing the payments or income or whatever.\n\nIt's not supposed to be x-y.  It's normally something used in an Excel sheet, for example.  Rate would be a cell, and Range would a range of cells with the payments.  It just looks like a normal formula.  Something like =NPV(A1, A2:A100) + B1
401272
How are you even sure that such a function exists? the numbers look very random.
11307
These problems are talking about composite functions, which is where the results of one function are input into the second.  Usually it's written with a small circle in between (I'll use gof(x)) and read "g of f of x".  Remember that the function closest to the variable is the one that acts on it first.\n\nOne helpful tool to use when you can't figure out a problem is simplifying it to a problem you've done before.  For example, if f(x)= 3x and g(x)=x^2 ("x squared") then the composition gof(x) means take the results of f(x) and put them into g(x).  \nSo then gof(x) = (3x)^2 = 9x^2.\n\nYour problem is a bit more complicated, but we can use the same process:  \n\ngof(x) would be g(ax-1) so \ngof(x) = (ax-1)^2 + 3(ax-1) + 1\nUse the distributive property to expand this to\ngof(x) = a^2x^2 - 2ax + 1 + 3ax - 3 + 1\nand combine like terms to get\ngof(x) = a^2x^2 + ax - 1   *\n\nSo far, we've done everything just from the definitions of g(x) and f(x).  Now we use the last piece of information we were given: \nthat gof(x) = 4x^2 + ax + b  *\nWe compare the coefficients on like terms of these two polynomials (with the stars) to determine that since a^2 must equal 4, \na = 2 and b = -1 (from comparison of the constant terms).\n\n\nSee if you can use a similar process for the second problem!
201840
what do you mean?\nhow to calculate their speed or wat?
628123
I can derive a formula. But I have to write it using MSWord. I cannot write it here. Give me your email id and I shall send the formula as attachment. My email id is psbhowmick@yahoo.com.
118419
they give the values of x where the function crosses the x axis. so when y=0, the function is at the x intercepts. this is useful to factor polynomials, or draw it   and stuff.
520091
First, evaluate these functions to understand what they mean. Here is a listing of n and f(n)\n\n0 1 2 3 4 5 6 ...\n0 2 4 6 8 10 12 ...\n\nHere is a listing of n and g(n):\n\n0 1 2 3 4 5 6 ...\n0 0 1 1 2 2 3 ...\n\nEvaluate g • f using g • f (n) = g(f(n)) to get its listing:\n\n0 1 2 3 4 5 6 ...\n0 1 2 3 4 5 6 ...\n\nwhich provides evidence for question (a). g(f(n)) = g(2n) = n, because 2n is even.\n\nThe listing of f • g is\n\n0 1 2 3 4 5 6...\n0 0 2 2 4 4 3 ...\n\nAnalyze f(g(n)) = 2 [n/2]. What happens when n is even, and when n is odd?\n\nA function, F, is injective if different values never map to the same value. Or, the listing does not have duplicates. To prove that F is not injective is easy: just find a counterexample, that is a and b such that F(a) = F(b), but a ≠ b. To prove that F is injective you must show that in general if F(x) = F(y) then x = y. \n\nLook at the listings. If a listing has duplicates then the function is not injective. A proof is just providing a counterexample. Example: f • g has duplicates; the simplest are 0 and 1: f • g(0) = f • g(1), and 0 ≠ 1.The listing of f has no duplicates. To prove that f is injective, prove that if 2x = 2y then x = y. That should be easy!\n\nA function is surjective if the listing contains every number in the domain, that is all the numbers: 0, 1, 2, 3,...\n\nThe listing of f does not contain 1. So f is not surjective. A proof is to show that there is no n such that f(n) = 1. That's easy because f(n) is even!\n\nThe listing of g appears to contain all the numbers. Does it contain 2006? Can you find n such that g(n) = 2006? Such that n/2 = 2006? Yes, n = 4012. Similarly, for any number (instead of 2006).\n\nSo, I have provided some strategies and examples to let you now make your own proofs.
413210
Your answer key is wrong, or you are not reading the right answer.\nFrom the data you presented above y = x^3 is OK.
217227
Properties of mathematics makes it work. I'm not sure exactly what it has you do but essentially it does this.\n\nIf your number is X. You add 5 to it then subtract 5 from it and you get your original number. Of course the nice ones hide the fact that your doing exactly this. \n\nDavid Copperfield did a TV bit once where he had a 3X3 square. You start out at any square you want and move according to his directions. After each move he took away a square. In the end you always end up on one square. That was cool. Anyone heard of it?
579711
f(x,y)= (1-x)^2 + 105 (y- x^2)^2\n\nIt's often used to test out various nonlinear optimization algorithms.
24951
The "domain" is the inputs, and the "range" is the outputs. If you were graphing them, the domain would be the x-axis, and the range would be the y-axis.
259902
I do not know about F.But I know (x).Does she have something like(3,4)(3,5)?\n\nx_|y_ <-- or does she have that?\n3, 4\n\ny=2f(x)\n4=2f(3)                          \n\n      ^\n      That's what she is supposed to do.\n      To solve the function.\n     But still i am sorry about not knowing F.\n    (Those # is example)
549578
The last link was the most informative.\nThe function is as follows:\n(x' y')T = [(1 1)T (1 -1)T] (x y)T\n\nIf you multiply the basis vectors by this matrix you get:\n(0 2)T for the (1 -1)T vector and\n(-1 -5)T for the (-3 2)T vector.\n\n(0, 2) = c1 * (1, -1) + c2 * (-3, 2)\nso:\n0 = c1 - 3 * c2\n2 = - c1 + 2 * c2\nc1 = -6\nc2 = -2\n\nlikewise:\n(-1, -5) = c3 * (1, -1) + c4 * (-3, 2)\nc3 = 17 and c4 = 6\n\nM = [(-6 -2)T (17 6)T]
579380
it's c\n\neven functions have the property that evaluating the function at their negative and positive values for the variable produces the same result.
447194
We're working on the domain [50,80].\n\nFor that domain, the rate per person is 200 - 2(x-50) = 300 - 2x\n\nYour total revenue is the rate per person times the number of people: (200 - 2x)x = 300x - 2x^2.\n\nYour profit is the revenue minus the total cost. Here, the cost has two components, a fixed cost and a variable cost.\n\nThe total cost is 6000 + 32x.\n\nTherefore, your profit function is (300x - 2x^2) - (6000 + 32x) =\n\nf(x) =  -6000 + 268x - 2x^2.\n\n To find the extrema of this function, take the first derivative and set it equal to zero. This isn't rigorous, but since f(x) is a parabola that points down, it will have a single extremum that must be a maximum. (You'd really have to use the second derivative test to verify this.) \n\nf'(x) = 268 - 4x = 0\n\n268 = 4x\n\nx = 67\n\nWith 67 people, the rate is $166. The revenue is $11122.\n\nThe costs are $6000 + 32*67 = $8144.\n\nThe profit is $2978.\n\nNote that the profit at x = 50 is $10000 - $7600 = $2400.\n\nThe profit at x = 80 is $11200 - $8560 = $2640.\n\nThis doesn't prove that we've found the maximum. But given what we know about f(x) - namely, that it's a parabola that points downward, we should expect that it's rising slowly enough for its vertex to be at an x-coordinate greater than x = 80, or that it peaks at a point between x = 50 and x = 80 that is closer x = 50 than it is to x = 80.\n\nJust as a second informal check, when x = 65, the revenue is $11050 and the costs are $8080, giving a profit of $2970.  Clearly, we're approaching the maximum that occurs at x = 67.
596795
Think about your order of operations. If you were evaluting the function for some number, what would you do first? That function is your *inside* function.
99703
1. {5.6, 8), (5.8, 6), (6, 5.8), (5,6}\n\n2. { (85,3), (95,11), (110,15), (110,20)}\n The domain is the set of all first coordinates, and the range is the set of all second coordinates.  A relation is a function if all the first coordinates are different.  So your second set of points is NOT a function (since two different points have the same first coordinate).