Is the following Kernel invertible? 

$K(x,y)=\frac{e^{-\frac{xy}{x+y}}}{x+y}, x\in[0,1],y\in [0, \infty)$

i.e. if
$\int\_0^1 K(x,y) f(x) dx=0 ,\forall y\in [0, \infty)$ can we conclude $f(x)=0,x\in [0,1]$?