MathNet 2004 — Part 02 Question 99

The following apply to the rational function $f(x)=\frac{a x+b}{c x+1}$: $f(1)=\frac{3}{4}$, $f(2)=1$ and $f(-1)=-\frac{1}{2}$. Determine the real parameters $a, b$ and $c$ and write the function $f(x)$. Function notation simplifies.