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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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How to do Inverse formulas/Rearrange formulas in Mathematica? [duplicate]

Hi am a student in chemical engineering and I have the necessity to rearrange formulas algebraically, for example ...
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Invert a transcendental function

I have tried Reduce and Solve in Mathematica, as well as have a long list of tries in Maple, but cannot seem to get anywhere ...
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Finding the InverseFunction of a polynomial function restricted to an interval [duplicate]

I want to calculate the inverse of f[x_] := 1/2 - (x (4 x^2 - 9))/12 /; -1/2 <= x <= 1/2 f[x] is monotonic inside $-0....
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1answer
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InverseFunction oddity

InverseFunction[ConditionalExpression[#, 0 <= # <= 1] &] InverseFunction[ConditionalExpression[#, -1 <= # <= 1] &] The first line produces ...
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Is there a way to symbolically invert a piecewise function

I have a piecewise function that is continuous and strictly monotonic, like this: f[t_] = Piecewise[{{t/4, t < 0}, {t/2, t < 3}, {3/2 + (t - 3)*3, True}}] ...
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Invert Colors Stylesheet White on Black

There have been a couple studies done that showed that white text on a black background increase recall of data. Although this is certainly debatable how might I invert the colors of Notebook font ...
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Need a generalization of RootApproximant to recognize linear combinations over algebraic numbers

RootApproximant does a very good job when I need to recognize an algebraic number and when enough of its digits are known (or even when an unlimited number of ...
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1answer
503 views

Inverse on a restricted domain

I have a function, whose domain is [0,1]. The function is f = Piecewise[{{Exp[-β * (-Log[#])^α], 0 < # <= 1}}, #]& with ...
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1answer
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InverseFunction on an Interpolating Function is misbehaving

I am getting strange behavior when I try to calculate the inverse of an interpolating function for two similar data sets. My data sets are: ...
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1answer
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Prandtl-Meyer function

I'm trying to solve for Mach number based on the given Prandtl-Meyer function, however I keep getting odd error. Here is my code: ...
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5answers
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Plotting the solutions to a transcendental equation

I am trying, to no avail, to use Mathematica to produce a plot in (x, y)-space of the solutions to the equation Cos[Sqrt[y]] + Sin[Sqrt[y]]/Sqrt[y] == Cos[x] ...
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1answer
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Efficient method for inverting a block tridiagonal matrix

Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix? For example: ...
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1answer
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How to get the determinant and inverse of a large sparse symmetric matrix?

For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
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Automatic inverse for Lambert’s Azimuthal Equal-Area Projection

I’m interested in finding closed-form inverses for map projection equations in general (of course, this is not always possible). I’m hoping Mathematica can help me with some of the trickier ones. As ...
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3answers
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How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
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1answer
833 views
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2answers
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How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
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Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
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2answers
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Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
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2answers
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How to invert an integral equation

There have been numerous times when I've needed to invert an integral equation, i.e. I have something like $$f(x) = g_1(x)\int_{0}^x g_2(x') dx'$$ for arbitrary functions $g_1$ and $g_2$, and ...
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3answers
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Changing variables algebraically

Suppose one has two functions, $y(x)$ and $z(x)$, and one seeks to obtain $y(z)$ by substituting $x(z)$ into $y(x)$. Can this be done in a single step? Or must $z(x)$ first be inverted independently? ...
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1answer
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Mathematica Can't Evaluate This?

I am trying to find the inverse function of $\frac{\ln{x}}{x^2}$ in Mathematica. I am using the Solve[] function to find the inverse (yes, I know about ...
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3answers
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How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, b,...