# 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.

1,036 questions
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### Finding an inverse function (sum of non-integer powers)

I have a function: $$f(x)=x^{2.2} + (1-x)^{2.2}$$ It is defined on the interval $[0,1]$. Minimum: $x=0.5, y=2*0.5^{2.2} = 2^{-1.2}$. I want to find an inverse for it. Since the function has two "...
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### Help with concepts with the inverse function theorem

I am solving the following problems: Be the transformation $T \in R ^ 2$: by $T(u, v) = (u ^ 2-v ^ 2, uv) = (x, y)$. Calculate the Jacobian of $T$ and conclude whether the transformation is ...
3answers
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### Show bijectivity of $f:(-1,1)\rightarrow \mathbb{R}, f(x)=\frac{x}{1-|x|}$

Show bijectivity of $f:(-1,1)\rightarrow \mathbb{R}, f(x)=\frac{x}{1-|x|}$ So in order to show injectivity $f(a)=f(b) \Rightarrow a=b$ so $\frac{a}{1-|a|}=\frac{b}{1-|b|}$. But how do I prove that? ...
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### If $f(0)=2$, $f'(0)=3$ and $g=f^{-1}$ then what is the value of $g'(2)$?

I know that $f(0)=2$, $f'(0)=3$ and $g=f^{-1}$. But how can I find the value of $g'(2)$?
0answers
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### Preimage Structures: lists of all inverse images at a given depth (reference request)

I am studying the list of inverse images (preimage sets) of some function $f$ at a given inverse depth $j$ -- for each element $x_i$ of a finite domain $X$. For example, the j-th such list would be ...
1answer
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### Inverse Fourier transform of $F(k) = 1/(k^2+a^2), a>0$

I need help finding the Inverse Fourier transform of: $$F(k) = \frac1{ k^2 + a^2 },~ a>0$$ Here is what I have so far: Singular points at $k^2 = a^2$, namely, at $k = \pm ia$. The inverse ...
1answer
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### Output response from closed loop transfer function using MATLAB

This transfer function is to control the position of Permanent Magnet DC motor. I was able to get the transfer function and now I need to analyze the output for the tuned closed loop for a given input ...
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### Continuity and Uniform Continuity of inverse functions

Let $f : X → Y$ be a given function, and suppose that $f^{-1}(C)$ is an open subset of $X$ whenever C is an open subset of $Y$ . (a) Prove that f is continuous on $X$. (b) Prove that $f^{-1}(B)$ is ...
1answer
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1answer
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