I am trying to find the inverse function of the following function , or prove that it does not have one , but I can't do either of those things.
$$ y(τ)= \int_{τ-1}^{τ+1} \cos(\frac{πt}{8})\,x(t) \,dt $$ where $x(t)$ is a function with the same domain as $y(t)$. Can someone help with finding its inverse function or proving it doesn't have one . Proving that it has one, can also help.
After evaluating the integral, we can see $y(t)$ is constant $\forall \ t$. Therefore, it has no inverse.