# Tagged Questions

Inverses include: multiplicative inverse of a number (reciprocal), inverse function, matrix inverse, etc. A subject tag such as (linear-algebra), (algebra-precalculus) or (arithmetic) should be added to clarify in which sense "inverse" is used. This tag should never be the only tag on a question.

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### Find the inverse function of $y=x|x|e^x$

I am having problems finding the inverse function of a complicated function. In this case: $$y=x|x|e^x$$ I thought I could 'split' this function but I'm not sure if that's the right way. for $y=x$ ...
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### Inverse of bounded linear transformation

I'm not in the mathematics field and not very comfortable with strict mathematical formalism. The information I find on the Internet includes so many technical terms that might take ages for me to ...
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### Additive basis of order n: Sets which allow every integer to be expressed as the sum of at most n members of that set. [closed]

Every integer can be expressed as the sum of at most 3 triangular numbers. That is, the set of triangular numbers is an additive basis of order 3. The sum of the inverse triangular numbers is 2. (1/1 +...
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### Higher derivatives of inverse functions (Multivariable Calculus)

Given the function $$(u,v) = f(x,y) = (x + y, x^2 - y^2)$$ I would like to compute the second partial derivative of $x$ with respect to $v$, at the point $(u,v) = (2,0)$. To calculate the ...
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### Inverse of a special matrix: controlabillability like matrix from control theory

Is there a way to find the first vector in the inverse of the following real matrix $$M = \begin{bmatrix}B^{T} \\ B^{T} A^{-1} \\ \vdots \\B^{T}A^{-(n-1)} \end{bmatrix}$$ as a function of $B$, $A$ ...
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### What is the Order of operations for finding the inverse of a function AND solving.

I have $y=4(x+2)^3$. So first part of taking the inverse is switching the variables $x$ and $y$ so you'd have $x=4(y+2)^3$. Why does the exponent $3$ get put in front of the square root symbol? The ...
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### Proving facts about the inverse of a matrix

Let A and B be matrices. Show that: $(A^{-1})^{-1} = A$ $(A^{T})^{-1} = (A^{-1})^{T}$ $(AB)^{-1} = B^{-1}A^{-1}$ I think I'm supposed to use the inverse property (That $AA^{-1} = I$, where I is ...
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### Will this function be odd?

Question: If $f:R\to R$ is an invertible function such that $f(x)$ and $f^{-1}(x)$ are symmetric about the line $y = -x$, then: A) $f(x)$ is odd B) $f(x)$ and $f^{-1}(x)$ may not be ...
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### Fermat's little theorem question: why isn't $a^p \equiv 1$?

Fermat's little theorem says that $a^p \equiv a \pmod p$. I have kind of a stupid question. Since $p \equiv 0\pmod p$, why isn't $a^p \equiv a^0 \equiv 1 \pmod p$ ?