Mathematics Stack Exchange
Mathematics Stack Exchange

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 $x$.

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How to find inverse of linear + sine function?

I am stuck with this function for couple of days. I wonder how to find the inverse of it. $y = x + A \sin(2 \pi(B-x))$ with A and B are constants. If you have solution, can you give me some hints? Thanks !
Bui Tuan Khai
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Analytic expression for inverse of function involving product of exponentials

Consider the function $f:(0,\infty)\to\mathbf{R}$ given by $$ f(\alpha) = 1-\prod_{k=0}^{n} (1-Ae^{-\alpha k})$$ where $0
David M.
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inverse of $y=\frac{5x-3}{2x+1}$

I have solved it as follows: $\displaystyle x=\frac{5y-3}{2y+1}$ $5y-3=2xy+x$ $5y-2xy=3+x$ $y(5-2x)=3+x$ $\displaystyle y=\frac{3+x}{5-2x}.$ $\displaystyle {f^{-1}}(x)=\frac{3+x}{5-2x}$ That is my answer. But On the screen, there appeared another…
user36339
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Solving for the inverse of $f(n)=\frac{2}{5}n^{2.5}+\frac{1}{2}n^{1.5}+\frac{1}{8}n^{0.5}+\frac{1}{1920}n^{-1.5}$

$$f(n)=\frac{2}{5}n^{2.5}+\frac{1}{2}n^{1.5}+\frac{1}{8}n^{0.5}+\frac{1}{1920}n^{-1.5}$$ the inverse I need is for all positive integers. Can someone either tell me how to get this functions inverse, or just give it to me? All I know about finding…
DeJeL
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inverting the function $f:A \rightarrow B$.

Suppose $A$ is the set of real numbers equal to or greater than 2, $B$ is the set of real numbers equal to or greater than 1, and the function $f: A \rightarrow B$ is defined by $f(x)=x^2-4x+5$. How can I find the inverse of the function and the…
Seth Killian
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inverse image of sets

prove or disprove If $f : X → Y$ is a injective function and $f(X) = Y$, then $f^{−1}(f(\{u\})) = \{u\}\quad\forall u∈ X$. After I worked in this statement I find it is true statement since $f(x)$ is one to one but I am not sure since I find that…
dr.rise
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is a monotonic function multiplied by an invertible function still invertible?

If we have an invertible function $f(x)$ defined on the Reals, and we have a strictly monotonic function $m(x)$ also defined on the Reals. Is $g(x):=m(x)f(x)$ then also an invertible function? Is there a simple proof for this? Edit: What if we…
user56834
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Interpreting question regarding intervals and inverse

How would you interpret "for each of the intervals I, give the domain and range of the restriction $f_{I}$ of $f$ to I and sketch the graph of the inverse of $f_{I}$ "? The intervals are (∞,0], [0,2] and [2,∞) and the equation of the function is…
randb
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Analytical Inverse function of exponential function of polynomials

How can I obtain the inverse of the function below analytically? $$e^{(0.0116t^2-0.4212t)},\ \ \ 0
YONGSEEN KIM
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Finding inverse polynomial function

I'm having problem solving this question and I was hoping someone could help me out a bit. This is what's given: $g(x)=x^3+x-9$ and I'm supposed to find $\ g^{-1}\left(1\right) $ Am I supposed to just find the inverse and just plug it in? If so,…
SmhConfused
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Solve the inverse of $y = \dfrac{2x+1}{3-4x}$

So I just got back from a Calculus test and I have some trouble figuring out one of the questions, it states: "Calculate the inverse of the function $y=\dfrac{2x+1}{3-4x}$." What first came into my mind was to eliminate the denominator somehow. But…
Salviati
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What are inverse functions?

Okay, so you have inverse functions: $ x^{2^{\frac{1}{2}}} = x$ But you also have negative functions $ x^{2^{-2}} \neq x$ But when I look for inverse functions, they are usually defined like this: $$ f^{-1} $$ However when I write $sin^{-1}(x)$, I…
hgiesel
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Inverse Functions of simple quadratics - simply disguised problem

Find the equation of the inverse of y = (x + 2)^2 - 4 Edit: Simply switching around the x and y doesn't work because then you are stuck with solving for y x = y^2 + 4y There should be a simpler method Edit: The domain is restricted to x is greater…
TripleA
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Inverse Functions and proving the product of derivatives is 1

Write down the derivative of the function y=x^3 - 1: 3x^2 Make x the subject and hence find dx/dy: 1/3(y+1)^-2/3 Show that dy/dx * dx/dy = 1 How does the x and y possibly cancel out? It seems like a very straightforward question but what do i do?
TripleA
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Inverse of a cubic function containing the sine function

The question I'm trying to solve requires me to get the $f^{-1}(x)$ where $f(x)= x^3 + 2x^2 + 4x + \sin (\pi x/2)$ , but I don't know to proceed with such problems with higher degrees of x (and the trigonometric functions don't help much either) .…
Keith
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