> 
> $f:[1,4]\to\mathcal {R}$ is a continuous function and $f(1) = f(4)$. Prove that there exists $x$ where $\mathcal { f(x) = f(x + 1.5)}$.
> 
> 
> 

I am unsure about how to proceed with the solution to this problem. Any hints are appreciated.

Thank you!