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# Questions tagged [inverse]

Questions on exact, symmetric reversal of a definition or functional mapping (i.e. the original form is returned when applied twice). Use this tag for issues on inversion of Mathematica expressions, or general inversion of math constructs.

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-1 votes
0 answers
42 views

• 1,001
1 vote
1 answer
127 views

### Trouble finding inverse of a function

I have the following Mathematica code: ...
• 2,513
1 vote
1 answer
163 views

### Newton method and Armijo-Goldstein

I need help with my project. I have three nonlinear systems and I need to write a code for Newton methods and Armijo-Goldstein and see the differences. ...
3 votes
5 answers
244 views

### Numerical solution of the inverse contour plot

I have a function $f(u,v)$ on some domain of $(u,v)$ and would like to find (numerically) the set of couples* $(u_0,v_0)$ s.t. $f(u_0,v_0)=0$, for instance (just and example to illustrate, in practice ...
8 votes
2 answers
420 views

### Asymptotic inverse function?

A paper I am reading defines a variable $\theta$ in terms of another variable $\phi$ as an expansion in $u$, where $u$ is understood to be small: $$\theta=\phi-u^2\sin\phi+\mathcal{O}(u^4).$$ They ...
• 183
7 votes
1 answer
207 views

### How to get more terms with the Series[] expansion of InverseErf[x] around x=1?

The inverse error function, which is given by InverseErf[x], is quite important in statistics as it gives the confidence levels around a 1D Gaussian, for example ...
• 1,848
8 votes
4 answers
1k views

### How can I find the inverse of an interpolating function?

I am numerically solving the coupled differential equations (for $t[\tau]$ and $r[\tau]$) below. Mathematica outputs two interpolating functions as solutions. I would like to invert one of these ...
• 181
4 votes
2 answers
1k views

### Inverse function of y = x + (0.022 - x) ^ 1.414?

I'm a software engineer with math classes through differential equations about 15 years in my past, and I've gotten stuck trying to invert an equation. The equation: $y = x + (0.022 - x)^{1.414}$. In ...
2 votes
1 answer
314 views

### Invert a generic n x n matrix

I want to invert a generic n x n matrix. Is it possible to do this with Mathematica? Consider, as a minimal example, the $n\times n$ matrix: \begin{bmatrix}1n&0&...&0\\0&2n& ... &...
• 251
0 votes
0 answers
153 views

### Variation with respect to inverse metric in a Lagrangian density

I am trying to vary the following Lagrangian density with respect to the inverse metric appearing in the equation, but I am having trouble with how to write the right code in Mathematica. I have ...
• 1
0 votes
0 answers
167 views

### Inverting function variables

The original equation is a function of x. However, I want to invert the function and get an expression of x in terms of y. ...
• 2,688
1 vote
2 answers
86 views

### Inverse Function for an example

I have this funtion i would like to calculate the inverse Inverse[Sqrt[1 - Cosh[2 t] + a Sinh[2 t]]] a is positive number.
• 457
0 votes
1 answer
94 views

### InverseFunction fails at some parameter

Currently, I am faced with the difficulty of evaluating the inverse of the function below for certain negative decimal values of the parameter q. Specifically for ...
• 181
1 vote
2 answers
180 views

### Plot the solution and Inverse as well

I used this code to solve an equation and now I would like to plot the solution with its inverse. I can't get some figures?!! ...
• 457
1 vote
1 answer
97 views

1 vote
0 answers
92 views

### Fail to inverse the Piecewise function embedded in a NDSolveValue

I am trying to estimate a function consisting of a Piecewise function that included in a FEM solver. I firstly developed my mesh for the FEM model based on @Tim Laska's work. The code is shown as <...
• 329
0 votes
0 answers
157 views

### Inverse Functions

I'm new to Mathematica, so I fell sorry for posting relativily naive/dumb questions. I have these two functions that represent X coordinate distortion of an SLA 3D printer. ...
• 417
5 votes
3 answers
114 views

### Does Solve make internally assumptions about the domain of the variables?

I recently tried to invert the innocent looking function $\frac{x}{(1+\sqrt{1-x})^2}$ So I tried the command Solve[x/(1 + Sqrt[1 - x])^2 == y, x], which ...
• 137
0 votes
0 answers
193 views

### Command to find the pre-image of a set that is mapped to by the function $f(x)=3^x \mod{17}$

$$f(x)=3^x \mod{17}$$ How to find the pre-image of the set if this function maps from real numbers to real numbers. What command would I use, to see the pre-image if the function would map from ...
• 241
2 votes
1 answer
87 views

### Inverse of the matrix with several indices

Suppose I have a square matrix $A_{mn}$ where $m=(i,j)$ and $n=(k,l)$. For example, if $i,j,k,l=1..N$ the matrix is $N^2\times N^2$. For simplicity, let me generate it by ...
3 votes
2 answers
362 views

### How to get x value where area under curve is some number?

My goal is to get x value where area under the curve (from the x ~ infinity) is about 0.05. But the code which I have tried shows errors. How to correct it? ...
• 648
0 votes
1 answer
102 views

### Getting inverse of x^2 with positive x

My goal it to get inverse of x^2 for positive x. But the result shows always minus -Sqrt[y]. How to correct ...
• 648
0 votes
1 answer
85 views

### Condition at Inverse function

My goal is to get inverse of -Log[1 - x]. But the result shows conditional expression. Could I know Why the condition -[Pi] <= Im[y] < [Pi] shows? There wass no assumption at variable y. ...
• 648
1 vote
1 answer
169 views

### Asymptotic expansion at infinity given a branch cut

Basically, I have obtained the function $\rho (r)$ below as a result of integrating $$\rho(r)=\int_{b_0}^{r}\frac{dx}{\sqrt{1-(b_{0}/x)^{1-q}}}$$ which results to ...
• 181
0 votes
0 answers
67 views

### How to return an inverse function based on parameters (for formal differentiation)

I want to return a different function for any given parameter in order to later calculate a value of the inverse of that function given the parameter as an indeterminate. That is, I want, for each $d$,...
• 101
0 votes
2 answers
86 views

### Plot Parametric f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x)

I want to plot f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x) f[x_] := 2 a ArcTanh[(# a)/Sqrt[-1 + #^2 b]] + a Log[1 + #^2 (a^2 - b)] - 2 Log[# b + Sqrt[-1 + #^2 b]] &...
0 votes
0 answers
32 views

### Plotting Inverse Function - more complicated [duplicate]

I would like to plot the inverse of $f$ using the same method that was suggested to me in my previous question: f[x_] := [(2 μ ArcTanh[(# μ)/Sqrt[-α + #^2 ν]] + μ Log[α + #^2 (μ^2 - ν)] - 2 Sqrt[ν]Log[...
5 votes
0 answers
84 views

2 votes
0 answers
42 views

### establish matrix and inversion of a uppertriangularized matrix [closed]

Trying to create an uppertriangularized matrix with Poisson Distribution, find its inverse and multiply the inverse by a vector, i.e. ...
• 497
3 votes
1 answer
105 views

### Inverse of DiracDelta at 0 is 99/5?

Here in this other question of mine I asked the question, but maybe here is more pertinent. When using Mathematica we can find the following result: ...
• 1,536
1 vote
2 answers
167 views

### Finding the inverse of possibly non-invertible interpolation function

Consider the following sample code pts = Table[{i, i^2}, {i, -10, 10}]; foo = Interpolation[pts]; Plot[InverseFunction[foo][y], {y, 0, 10}] From the plot, we see ...
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