Question 157
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfies
$$
f(x)+f(y)=f(x) f(y)+1-\frac{4}{x y}
$$
for all nonzero real numbers $x$ and $y$. Given that $f(1)\gt 0$, find the value of $f(4)$.
$$
f(x)+f(y)=f(x) f(y)+1-\frac{4}{x y}
$$
for all nonzero real numbers $x$ and $y$. Given that $f(1)\gt 0$, find the value of $f(4)$.