Let $$g(x)=\cos(x^5)+\sin(x^2)$$ If we were to have a Fourier Series representation of this function $$g(x)=a_0+\sum_{n=1}^{\infty}\left(a_n\cos(n\omega_ot)+b_n\sin(n\omega_ot)\right)$$ The question is: Which of its coefficients would be zero?
When I graph this in Desmos, I seem to get a non-periodic function and Symbolab seems to agree with my assumption. We are not given a period or a 'window' in the question either but the solution suggests that since $g(x)$ is an even function $b_n=0$ and $a_n$ can have a non-zero value. How can we even have a Fourier Series representation if the function does not have a period or a given 'window'?
(This is not a homework or a quiz question.).