Question 148
Find all functions $f : \mathbb{R} \to \mathbb{R}$ with the property that
$$
f(x)f(y) = (xy - 1)^2 f\left(\frac{x+y-1}{xy-1}\right)
$$
for all real numbers $x, y$ with $xy \neq 1$.
$$
f(x)f(y) = (xy - 1)^2 f\left(\frac{x+y-1}{xy-1}\right)
$$
for all real numbers $x, y$ with $xy \neq 1$.