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.

In mathematics, an inverse function or $f^{-1}$ is a function that "reverses" another function. That is, if $f$ is a function mapping $x$ to $y$, then the inverse function of $f$ maps $y$ back to $x$.

2219 questions

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Finding x from Inverse Circular Function equation

Find $x$ when $\sin^{-1}(x)+\sin^{-1}(1-x)=\cos^{-1}(x)$ I guess it's based on some trick

inverse-function

asked Nov 16 '16 at 02:54

Ashish

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0 answers

Showing 1-1 and invertiblity of a function

Given an invertible function $f: \mathbb R ^n \rightarrow \mathbb R ^m$, how can we show that it is one to one and invertible? Given an example such as $f(x,y) = (y + x,\sin y ,yx)$, what can we conclude? If this was a function that took $(x,y)…

inverse-function

asked Sep 28 '16 at 06:22

Astrum

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0 answers

Inverse of $f(x)=x^{0.2}+x^{0.5}$

I have tried extensively to find the inverse of $f(x)=x^{0.2}+x^{0.5}$, but to no avail. I asked my algebra professor, and she didn't know either. I put the question into Wolfram Alpha, but it said "no results found in terms of standard…

inverse-function

asked Sep 21 '16 at 19:16

Daniel Williams

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2 answers

Computing the inverse of $n^{n^2}e^{-n^2}$

What is the method for computing the inverse of this function? I'm interested in asymptotic approximation. We can consider that $n \in \mathbb{R}$. Thank you very much.

inverse-function

asked Jun 18 '16 at 09:02

Dingo13

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1 answer

Inverse of a particular function

How can we compute the inverse of the function $$f(n)=\frac{a^{n(n+1)}}{b^n}$$ where $a$ and $b$ are positive constants?

inverse-function

asked Jun 14 '16 at 14:29

Dingo13

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2 answers

Inverse function Khan Academy

I'm doing an exercise on inverse functions on Khan Academy and cannot get with the first exercise. Where to find number $93$? There is no such number in the table...

inverse-function

asked Mar 19 '16 at 07:28

NZMAI

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Understanding Injective, surjective and bijective in terms of marraige proposal?

I think this is easier to understand the mapping of injective, surjective and bijective in terms of marraige proposal where men are from set A and women from set B but Is this analogy correct? Injective (One-to-One) Functions: If the marriage…

inverse-function

asked Sep 28 '23 at 10:20

munish

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2 answers

How do you find the inverse function of $f(x)=e^{2x}+4x^3$?

So the first thing I found is if the function is one-to-one, because we know that if it is there is a inverse function of that function: I found the derivative of the function: $f'(x)=2e^{2x}+12x^2$ where $f'(x) > 0$ for $x \in (-∞,∞)$ which…

inverse-function

asked Mar 14 '23 at 09:36

SliVetle

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4 answers

If $n$ is even, prove $P(x)$ cannot have an inverse function

If $P(x)$ is a polynomial of degree $n$, how can I prove that if $n$ is even, $P(x)$ cannot have an inverse function.

inverse-function

asked Feb 02 '21 at 20:08

user38372

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3 answers

Inverse function of a piecewise polynomial

What is the inverse function of $f:\mathbb R\to\mathbb R$ with $$f(x)=\begin{cases} x^2&x\ge0\\ -x&x<0\end{cases}$$ I have trouble finding inverse function. For some outputs such as $25$ I am not able to determine which condition did it satisfy.

inverse-function

asked Jul 06 '19 at 11:24

Mathematical Curiosity

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1 answer

Finding the inverse function

Let $X=\{3, 5, 7, 10\}$ and let $Y=\{\text{fish}, \text{lion}, \text{penguin}, \text{cow}\}$ Let $f$ be a function from $X$ to $Y$ defined by $f(3)=$ lion, $f(5)=$ cow, $f(7)=$ fish, $f(10)=$ penguin The function $f$ is an inverse function.…

inverse-function

asked Aug 27 '17 at 23:46