$($IV$)$ Consider pairs functions on the domain xin$[-,]($i$.$e$.,$ in the entire $1$D space$)$:

$(x)-=e^{-\frac{1}{2}{x}^2},f(x)-=(x^3-1)e^{-\frac{1}{2}{x}^2},g(x)-=(x^3-x)e^{-\frac{1}{2}{x}^2},h(x)-=sin(2x)$

Argue whether $$ is orthogonal to all the remaining functions $f,g,$ and $h.$ Note that you do not need to compute all the integrals! $($It is helpful if you sketch the functions by hand$)$