Scaling fractions

Question

I have a set of values between $0$ and $1$ inclusive and I want to scale them so that they are all between $0.5$ and $1$ inclusive. What function can I use to do this?

\begin{align} f(0) &\to 0.5\\ f(0.5) &\to 0.75\\ f(1) &\to 1 \end{align}

Answer 1

Assuming you want this scale to be linear, use $$ f(x) = 0.5 + 0.5x = \frac{1+x}{2} $$