CAN U TELL THE INVERSE OF

X-SIN(X)?

THANK U

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- Sep 1st 2008, 07:43 AMADARSHwhat's inverse of this function?
CAN U TELL THE INVERSE OF

X-SIN(X)?

THANK U - Sep 1st 2008, 07:50 AMSoroban
Hello, ADARSH!

First of all, release your CAPS LOCK . . .

All upper-case is**very**annoying ... and juvenile.

Quote:

Can you tell the inverse of: .$\displaystyle f(x) \:=\:x-\sin(x)$ ? . . . . no

We are required to solve for $\displaystyle y\!:\;\;y - \sin y \:=\:x$

This is a*transcendental*equaton . . . there is no elementary solution.

- Sep 6th 2008, 04:39 AMADARSH
I have recieved the answer as

$\displaystyle

X+sin(X)

$

Its mirror image

of $\displaystyle X-sin(X)$about $\displaystyle x=y$ - Sep 6th 2008, 09:04 AMskeeter
- Sep 6th 2008, 03:25 PMPlato
Before I continue, let me say how dumb I think this question/answer is.

However, the posted answer is in fact correct.

If you graph the inverse correctly it is easy to see.

The reflection in the line y=x is $\displaystyle (x,y) \to (y,x)$. - Sep 6th 2008, 04:10 PMskeeter
are you saying that $\displaystyle y = x+\sin{x}$ is the inverse of $\displaystyle y = x-\sin{x}$ ?

here is a correct graph of $\displaystyle y = x-\sin{x}$ and its inverse $\displaystyle x = y-\sin{y}$ ...

http://i39.photobucket.com/albums/e1...hn/inverse.jpg - Sep 7th 2008, 10:10 PMADARSH
I also got the same graph as Skeeter fr$\displaystyle x+sinx$

and that's why I posted this quest.

if reflection abt

$\displaystyle x=y $always the inverse

than wat abt

$\displaystyle sinx-x$ - Sep 8th 2008, 08:04 AMPlato
Absolutely not! Soroban has is correct. There is no elementary inverse possible.

However, in parametric form $\displaystyle \left( {t,t + \sin (t)} \right)\,\& \,\left( {t + \sin (t),t} \right)$ are reflections of each other in the line $\displaystyle y=x$ and as such act as an inverse.

In this new graphic, that point is illustrated using $\displaystyle t=2$. - Sep 8th 2008, 04:09 PMskeeter
my mistake ...

when you said

Quote:

However, the posted answer is in fact correct.