# Thread: what's inverse of this function?

1. ## what's inverse of this function?

CAN U TELL THE INVERSE OF
X-SIN(X)?
THANK U

First of all, release your CAPS LOCK . . .
All upper-case is very annoying ... and juvenile.

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.

3. I have recieved the answer as
$\displaystyle X+sin(X)$
Its mirror image
of $\displaystyle X-sin(X)$about $\displaystyle x=y$

I have recieved the answer as
$\displaystyle X+sin(X)$
Its mirror image
of $\displaystyle X-sin(X)$about $\displaystyle x=y$
is that so?

5. 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 $\displaystyle (x,y) \to (y,x)$.

6. 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 $\displaystyle x = y-\sin{y}$ ...

7. 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
$\displaystyle sinx-x$

8. Originally Posted by skeeter
are you saying that $\displaystyle y = x+\sin{x}$ is the inverse of $\displaystyle y = x-\sin{x}$ ?
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 $\displaystyle t=2$.

9. my mistake ...

when you said

However, the posted answer is in fact correct.
I thought you were talking about the OP's response to Soroban's response.