All Questions
Tagged with applications functions
29
questions
9
votes
4
answers
460
views
"Class" of functions whose inverse, where defined, is the same "class"
Please excuse the amateurish use of the term "class", I don't know what the exact term is for what I'm looking for.
Anyway, details.
I'm asking specifically about real-valued functions on the real ...
- 101
6
votes
2
answers
15k
views
What are functions used for?
When I say functions, I don't mean the trigonometric functions like $\sin$, $\cos$, and $\tan$, I mean defined functions like $f(x) = 2x + 4$. Why is $f(x)$ used and why isn't a single variable ...
- 4,287
4
votes
6
answers
693
views
Is $x^3$ really an increasing function for all intervals?
I had an argument with my maths teacher today...
He says, along with another classmate of mine that $x^3$ is increasing for all intervals. I argue that it isn't.
If we look at conditions for ...
- 45
3
votes
2
answers
127
views
How are the functions determined for real-world applications (business, population models, etc.) of calculus?
The following problem has been taken from Paul's Online Notes:
"We need to enclose a rectangular field with a fence. We have 500 feet of fencing material and a building is on one side of the ...
- 33
3
votes
1
answer
134
views
A "perfect" (chess) rating system
Assume we want to have a player rating system with the following conditions:
For simplicity, no draws.
If A wins against B with ratings $a,b$, their new ratings are $a'=f(a,b),b'=g(a,b)$.
Most ...
- 745
3
votes
1
answer
67
views
Seemingly conflicting notions of a function
Throughout my mathematical education, I have seen a few, seemingly, different and conflicting notions of what a function is:
A function is a a type of mathematical object that maps every element of a ...
user997478
2
votes
2
answers
212
views
Function application (word problem)
The problem:
My work so far:
$3=log(\frac{A}{A_0})$--->$10^3=\frac{A}{A_0}$
$\frac{A}{A_0}=1000$
(Am I done there?)
Plugging it in:
$M=log(\frac{1900000}{1000})$
$10^M = \frac{1900000}{1000}$
$M=3....
- 309
2
votes
2
answers
390
views
An injective map where each value is mapped to many others?
I want "something" ("something" because maybe it is not really a mathematical function, called F in the above image) that can describe what is shown on the image. A given value from a domain Xi can be ...
- 1,072
1
vote
2
answers
1k
views
What is the simplest $\Bbb{R}\to\Bbb{R}$ function with two peaks and a valley?
What is the simplest $\Bbb{R}\to\Bbb{R}$ function with two peaks and a valley?
I have a set of points in $\Bbb{R^2}$ and I would like to fit a curve to the points, the points approximately lie on a ...
- 1,058
1
vote
1
answer
52
views
Unit decomposition by three continuous functions
My current research project involves adaptive weights for three different loss functions so that I hope each the objective can focus on the different size of objects when given a different size of the ...
- 255
1
vote
1
answer
103
views
Production functions total cost
Production function is: $f(L,M)=L^{1/2}M^{1/2}$. L is the number of units of labour, M of machines used. Cost of labour is 9 per unit, whereas the cost of machine is 81 per unit. Total cost of ...
- 1,141
1
vote
1
answer
46
views
How to write this function?
I do not want the answer given to me, I just want assistance.
Problem: Marcus invests $750 in an account that pays 9.8% interest compounded annually. Write a function that describes the account ...
- 309
1
vote
2
answers
56
views
How to use the properties of the logarithmic function
I'm coding the game asteroids. I want to make a levels manager who can create a infinity number of level increasing in difficulty.
My levels have as parameters :
The number of asteroids on the board;...
- 1,620
1
vote
2
answers
61
views
Is there any way to find out how many intervals greater than x exist in a list of values?
I'm not a professional mathematics, but I have a problem of applied mathematics. Beforehand, I apologize for not using more technical terms. I hope I can be as clear as possible:
Given the following ...
- 179
1
vote
0
answers
72
views
How units didn't change while differentiation?
In this example, rate of change has units cm², while the original quantity, area, also has same units. I learnt that units change just like normal ratio, that is dA/dr will have same units as A/r, so ...
- 61