Homework problem I'm having trouble with: find an explicit bijection $f: (20,21) \rightarrow (17,76).$ (open intervals in $\mathbb{R}$)
I tried to find the equation of a line between these two points in the XY plane and got $f(x) = \frac{-55}{3}x+ \frac{1163}{3}$, but this wasn't correct.
Is simply finding the equation of a line here the best approach? If so, what did I do wrong?
Thank you!
Best Answer
Rather than finding a map taking $20$ to $21$ and $17$ to $76$,
you should find a map taking $20$ to $17$ and $21$ to $76$.
The scale factor is $\dfrac{76-17}{21-20}=59$, so the answer is $f(x)=59(x-20)+17$,
which I leave to you to simplify.