I'm told that if $m<n$, then the intervals $(0,1)$ and $(m,n)$ are equinumerous.
I'm asked to prove this by exhibiting a specific bijection between them. I came up with this: $$f(x)=(n-m)x+m,\quad\text{for $0<x<1$}.$$
Is this a good function to choose?
As the main question has already been answered in the comments, here's a summary:
Yes, this is a good function to use. Because we can explicitly write the inverse as a function, we know that $f$ is a bijection.