Given $\frac{1}{4}\int_{-\infty}^{\infty} \frac{g_0(y)-f_0(y)}{\mu_0-\delta_R(y)}dy=1$
Is there any way to get such a representation
$g_0(y)=f(f_0(y),\mu_0,\delta_R(y))$
Here $g_0(y)$ and $f_0(y)$ are some density functions $\mu_0$ is a positive real number and $\delta_R(y)\in[0,1]$
Thanks alot.