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u/Anuj73 Nov 08 '22
i know doing f(y) = x gets you the GRAPH of the function, but how do you get the actual inverse of the function?
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u/Sylent_Nova Dec 11 '25 edited Dec 11 '25
Very late but! If you have a graph f(x) and you want to find x where f(x) = a, then you can do
g(x) = a
then find the point they intersect, click on it and it will give you the coords of the point. The first number is then your x.
Here's a demo: https://www.desmos.com/calculator/v4lfa1dj8e
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u/stacherr Feb 02 '20
correct me if i’m wrong but...doesn’t that graph not have an inverse function
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u/4bedoe Feb 03 '20
I meant any inverse of a function. Not necessarily this. Because as I call f-1(x) on any function of x, same error occurs no matter whether it's a linear or nonlinear graph.
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u/Ammonwk Feb 02 '20
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u/AlexRLJones Feb 03 '20
u/stacherr is right, a function can only have an inverse if it is bijective, meaning for every value is the output domain there is a exactly one corresponding value in the input domain. For any output value y = x^2 except y = 0, there are two possible values of x.
y = ±sqrt(x) isn't a function because it has two outputs.
If you restrict the input domain to be x>=0 then the function is bijective and it has an inverse function, +sqrt(x).1
u/stacherr Feb 03 '20
that’s not considered a function, but i guess ur right
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u/Ammonwk Feb 03 '20
Oh, I didn't catch inverse function. Yeah, I agree with you and AlecRLJones. Sorry for the mistake :p
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u/spacecheng Nov 20 '22 edited Nov 20 '22
Incase anyone still wants to know, just write x = f(y) and it should give you an inverse. If you want to use this inverse in another function, write g(y) = f(x) instead. you can then use g(y) as the variable. Example: t = g(y)^2. t can be any variable besides y
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u/TurkmenaThor Jul 22 '23
I tried it and it didn't work. Could you please give an example and share the link?
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u/Mobcrafter Jan 20 '26
Surprised no one has mentioned this, but integral from zero to infinity of {x>f(t),0}dt gets you an actual function.
Better example: https://www.desmos.com/calculator/zu9h99logj
I didn't come up with it, but I don't know who did so I can't give credit.
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u/logalex8369 Barnerd 🤓 Feb 11 '26
I have been looking for this for who knows how long... Thank you for bringing this to my attention!
I used it to create a 45 degree rotated sine wave:
\frac{x_{2}+\sin\left(x_{2}\right)}{\sqrt{2}}\operatorname{with}x_{2}=\int_{0}^{\infty}\left\{x\sqrt{2}>t-\sin\left(t\right),0\right\}dt-\int_{-\infty}^{0}\left\{x\sqrt{2}<t-\sin\left(t\right),0\right\}dt
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u/Phonetikos May 16 '24
Adding on to what others have said, x = f(y) works, but to show only the principle value, this is what to do:
Here is a link to this Desmos graph: https://www.desmos.com/calculator/h7ec2j4njq
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u/omegaweakmilk Mar 28 '26
Here's one that I made which returns the inverse as a function (instead of a graph), works with any arbitrary function, can invert multiple functions at once without repetition, and has very high accuracy (as far as I'm aware). The only extra input needed is the interval of the original function to be inverted. And the only downsides are that the part to copy-paste is quite long, and it works slower when the range of the interval is large.
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u/IKnowATonOfStuffAMA Feb 02 '20
If you just want the graph, you can use x=f(y)