Please help with finding an output for this function $f(x)=2|x-1|+|x+1|$ after injecting an interval $A=(0,2]$ to this function Please help with finding an output for this function $f(x)=2|x-1|+|x+1|$ after injecting an interval $A=]0,2]$ to this function. The domain of this function is natural.
To solve this, I would normally make X to be defined by an expression with Y in it ,but I do not know how to do that here because there is an absolute value of X only.

Hint


*

*Look at the values $f_{(-\infty,-1]}, f_{[-1,1]}, f_{[1, \infty)}$ of $f$ on each of the intervals $(-\infty,-1], [-1,1], [1, \infty)$ as those are the ones where you can get rid of the absolute values.

*On each of those intervals $f$ is linear, nice functions!

*Compute $A_1=f[(0,1]]$ and $A_2=f([1,2]]$

*Finally use the fact that $f[A]= A_1 \cup A_2$ to get the result you're looking for.


Good luck!
