# orthogonal function and inner product space

Consider the inner product space $$\langle f,g \rangle= \int_{-1}^{1} f(x) g(x) \ dx$$

find the non zero orthogonal function with respect to $$f(x)=1$$ in the subspace span of $${1,e^{x}}$$ ?

• hi please use LaTeX as I did right now. Also please make sure the notation corresponds to your true question. – Ahmad Bazzi Jan 31 '19 at 19:26
• -1 to 1 is the interval. can you add it too? – Allic Mendonca Jan 31 '19 at 19:27

If you compute the orthogonal projektion $$P(e^x)$$ on span(1). Then $$e^x - P(e^x)$$ is in the orthogonal complement of span(1).