Tagged Questions
2
votes
0answers
51 views
Perhaps an easy algebra problem, but it still evades me
I need help spotting a corresponding transformation
Let $x,y$ be some variables and $$z=z(x,y)$$. We have a transformation $X(\lambda):(x,y,z)\to (x',y',z')$, such that
$$x'= x\exp(a\lambda)\\
...
0
votes
0answers
13 views
Generalization/abstraction of an allocation problem
I'm having difficulty generalizing and finding the right abstraction for the following real world problem :
For each period, on a global segment, I know some data that is divided into intermediate ...
-3
votes
1answer
47 views
Separating $x_1^{x_2}$ into sum of two terms by variable transformation
Given the function $f(x_1, x_2)$ in the form of product of two variables.
$$f(x_1, x_2) = x_1^{x_2}$$
I want to apply a variable transformation on this function, so that I can write it sum or ...
2
votes
2answers
56 views
question on transformation
If a $2$d coordinate transformation function is given by $f(x,y)= 3x+1$, then what does it mean? How do I calculate the transformed coordinates for the points say $(3,4)$ in the initial space?
1
vote
1answer
41 views
Coordinate transformation to get even function
Suppose I have the function
$$f(y)=2y^4-5y^3+3y^2,$$
with zeroes $y=0$ (2x), $y=1$, $y=3/2$, which I only need on the part of the domain $0\le y\le 1$.
Is there a transformation $y\rightarrow y'$, ...
1
vote
1answer
140 views
Translating Cubic with Algebra?
I'm having a little trouble figuring out how to translate $ax^3+bx^2+cx+d=y$ by vector $(1,1)$ using only algebra. If possible could someone give me a hand?
An example:
Translate ...
0
votes
2answers
123 views
Transform/approximate this expression to avoid undefined value
I have an expression like this
$$\sum_i^n\log\frac{x_i}{y_i}+\alpha\sum_i^nx_i\log\frac{x_i}{\beta}$$
A potential problem is that $x_i$ and $y_i$ may take value $0$ for certain $i$, hence making ...
1
vote
2answers
159 views
Graphing Transformations. Why does the +2 in $f(x) = \sqrt{-x + 2}$ not work as expected when done out of order?
Graphing $f(x) = \sqrt{-x + 2}$ from the graph of $y=\sqrt{x}$.
Correct Method
First graph $f(x) = \sqrt{x}$.
then $f(x) = \sqrt{x+2}$ (shift left 2)
then $f(x) = \sqrt{-x+2}$ (Reflect over ...
1
vote
2answers
104 views
Arithmetic error when calculating inverse of the logistic?
I would like to rearrange the logistic function:
$$y=\frac1{1+\exp(-a+bx)}$$
To calculate $x=f(y)$
So I did the following:
$$\frac1{y}=1+\exp(-a+bx)$$
$$\ln\left(\frac1{y}-1\right)=-a+bx$$
...
