Assume I must solve the boundary value problem (BVP)
$$ -y''(x)+f(x)y(x)=g(x), $$
with $y(0)=0$ and $y(a)=0$.
The function $ g(x)$ is defined and known, but the function $ f(x)$ is defined implicitly by $$ f^{-1}(x)=h(x), $$ for a known function $ h(x)$.
My question is - if the function $f(x)$ is defined implicitly, how can we numerically approximate the BVP?