Let $V=\{h:[-1,1]\rightarrow\mathbb{R}\ \bigr|\ h\text{ is continuous}\}$.

Then we may define an inner product on $V$ by $\displaystyle\langle f,g\rangle=\int_{-1}^{1}f(x)g(x)\, dx$.

Which pair of vectors (functions) are orthogonal with respect to this inner product?