# Questions tagged [inverse-function]

For questions regarding an inverse function as the dominant topic of the post, or for questions requesting guidance on finding the inverse function for a particular function.

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### Multiplying by $1$ adds a solution to an equation

I have a question, which is motivated by my book's solution to finding the inverse function of $f(x)=\frac{x}{1-x^2}$ with the domain of $f(x)$ restricted the open interval $(-1,1)$. The questions are ...
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### Local invertibility of

Please check my understanding. (a) Let $f:\mathbb{R^2}\to\mathbb{R^2}$ defined by $F(x,y)=(x^2-y^2, 2xy)$. Calculate derivative matrix of $F$ and show $F$ is locally invertible except possibly at the ...
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### finding the inverse of a function from $M_2(R).$

I am trying to prove that the given map below is a diffeomorphism and it is pretty clear to me that it is a bijection but I do not know how to show that the inverse of the given map is smooth? in fact ...
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### Inverting a cubed root equation with two cube roots

In a recent StackOverflow question, I came across this formula: $$up = (1 + p)^\frac{2}3 - (1 - p)^\frac{2}3$$ and the question required the poster ...
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### Efficient way of determining inverse of conformal complex function numerically

I am wondering if there is an efficient method to compute the inverse of a complex function numerically. More precisely I have a certain amount of points $x_1,\ldots,x_n$ in the upper complex half ...
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### Chapter 12 Spivak Calculus: Spivak's comments about implicit differentiation

There is a passage in the Chapter 12 exercises of Spivak's Calculus (which is a book specific to real-valued functions) that reads as follows: In general, determining on what intervals a ...
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