Problem: Conditional pdf is marginal if X, Y are independent

Problem

\(X,Y\) are two independent continuous random variables with joint probability density function \(f(x,y)\) and marginal probability density functions \(f_X(x)\) and \(f_Y\left( y \right)\) . Show that

\[f_{X|Y}\left( y \right)=f_X\left( x \right)\]