# 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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### The integral of this horrible looking expression [closed]

Whats the $$\int (\cos(\tan^{-1}(\sin(\cot^{-1}x))))^2dx$$ no idea what to substitute already this is looking bad and that square is making things worse. Please help Thanks!!
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### Inverse Fourier Transforms

Find the inverse Fourier transform of the following: $$\sin(2 \pi \nu T) \cos (10 \pi \nu T) / (\nu T)$$ Attempt: I was told it was easier if we rewrite this in terms of a $sinc$ function. I think ...
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### Orthogonal matrix problem

So the question asks: Let $A$ and $B$ be n×nn×n orthogonal matrices, with $n≥2$. Which of the following matrices must be orthogonal? A. $A^TB$ B. The matrix C obtained by multiplying the second ...
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### Show that Ax = b is solvable when [A b] is singular.

I have the following problem: Review: Suppose A is 5 by 4 with rank 4. Show that Ax = b has no solution when, the 5 by 5 matrix [A b] is invertible. Show that Ax = b is solvable when [A b] is ...
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### Invertible function that “messes” order [closed]

I am looking for an invertible discrete function $f$ such that given some integer n, if i apply $f(i)$ for $i=0,\dots,n$ I would get all the integers in range $[0..n)$ exactly once, but in a "messy" - ...
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### Inverse Functions (Discrete Math)

Say you have $f: \mathbb{Z} \to \mathbb{Z}$ defined by $f(x,y) = (2x+y, y)$ How would you check if the function was invertible? As well as determining it's inverse if it is? Thank you
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### How can I invert the asymptotic form $x^{3/2}=y^{3/2}(1+a/y^2 + … )$ to find $y=y(x)$?

This might sound silly, but the fact there's a $a/y^2$ term in the expansion made me feel a little lost. Could anyone help? Thanks
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### When left inverse of a function is injective

Consider function $f^{-1}$ which is a left inverse of another function $f$. I require that $f^{-1}$ must be injective. What does it tell me about $f$? In other words, can I put some constraints on $f$ ...
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### Need two functions always be composed to prove they are inverses?

Normally, if I claimed that $f: A \rightarrow B$ and $g: B \rightarrow A$ were inverses of each other, I would check for the following results: $f \circ g(b) = b$ and $g \circ f(a) = a$. Suppose I ...
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### Calculating the inverse with variables that include logarithm and don't.

I am trying to calculate the inverse of this function and failing. $y_1 =z_1 \sqrt\frac{-2* log(z_1^2 + z_2^2)}{(z_1^2 + z_2^2)}$ Is there a systematic way to go about it?
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### Matrix computation of products

If I have two $n \times n$ matrices $A$ and $B$ and a vector $c$,how would I compute the product of $A^{-1}Bc$ ? I know how how to get $A^{-1}$ by doing LU decomposition of $A$ but how do I translate ...
Let's suppose that a real matrix $\textbf{A}_{n\times n}$ is nonsingular and its inverse is $\textbf{A}^{-1}_{n\times n}$. Next we change its $A_{ij}$ element to $A_{ij}+a$ and we keep all the other ...