Chapter 5.1, Problem 17P

Let $V=C^0\left[-1,0\right]$ and for $f$ and $g$ in $V$, consider the mapping

$\langle f,g\rangle ={\displaystyle {\int }_{-1}^{0}xf\left(x\right)g\left(x\right)dx}$.

Does this define a valid inner product on $V$? Show why or why not.