IMC 2002 — Keystage 3 (IWYMIC) — team Question 2

Let $f(x)=\frac{bx+1}{2x+a}$, where $a,b$ are constants with $ab\ne2$. (a) If $f(x)f(1/x)=k$ for all admissible $x$, find $k$. (b) Prove that $f(f(x))$ is not a constant function.