i wonder how i what the inverse function to f(x) = 2x - 3-| x - 3 | looks lika and how I salve it
For $\displaystyle x\le 3$ (I don't see any reason to include the "$\displaystyle 0\le x$")
x- 3< 0 so |x- 3|= -(x-3). Then f(x)= 2x- 3- |x- 3|= 2x- 3+ (x- 3)= 3x- 6 so that $\displaystyle f^{-1}(x)= \frac{x+ 6}{3}= \frac{x}{3}+ 2$ as chi-sigma said.
For $\displaystyle x\ge 3$, |x- 3|= x- 3 so that
f(x)= 2x - 3-| x - 3 |= 2x- 3- (x- 3)= x which has inverse $\displaystyle f(x)= x$.
Of course, neither of those answers the question "what is the inverse of ?"