CAN U TELL THE INVERSE OF
X-SIN(X)?
THANK U
Hello, ADARSH!
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.
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 $\displaystyle (x,y) \to (y,x)$.
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 $\displaystyle t=2$.