How to find all $f \in V$ such that $(\int_0^{\ln3}e^x f(x) dx)^2 \leq 2 \int_0^{\\ln 3} e^x [f(x)]^2 dx $
$V$ is a inner product space where $\langle f,g \rangle = \int_0^{\ln3}e^x f(x) g(x)dx$
I know this is a Cauchy-schwarz inequality and I'm able to prove it, but how to find f?