Find two continuous, increasing functions $f,g$ such that $f(x) = g(x)$ precisely when $x \in \mathbb{Z}$ Find two continuous, increasing functions $f,g$ such that $f(x) = g(x)$ precisely when $x \in \mathbb{Z}$
I'm pretty lost as to how to go about proving this. I feel like maybe it's going to be some sort of step function, but I'm not sure where to start. Any help would be appreciated.

One possible solution is given by $f(x)=4x$ and $g(x)=4x+\sin (\pi x).$
