I am looking for a transformation (and the inverse of that transformation) that takes $[a,b]$ into $[-h,h]$ (where $a$, $b$, $h$ are given and are different real numbers).
I tried doing this and got: $T(x)= 2h(x-a)/(b-a)$
I am looking for a transformation (and the inverse of that transformation) that takes $[a,b]$ into $[-h,h]$ (where $a$, $b$, $h$ are given and are different real numbers).I tried doing this and got: $T(x)= 2h(x-a)/(b-a) - h$.
It holds that $T(a)=0-h=-h$, $T(b)=2h-h=h$. I tried finding $T^{-1}$ and got $T^{-1}(x)=[(b-a)/2h][h+x+2ha/(b-a)]$.
But when I composed I didn't get the Id function.
What is the transformation to doing this ? (I think I got only $T^{-1}$ wrong, but I'm not sure).
**I was unsure about the tags - I tagged as linear algebra though the transformation is also have a translation in it, if anyone have a better idea for a tag tell me so I can change it.