Must a continuous function [math]f:\mathbb{R}^n\to \mathbb{R}(n>1)[/math], such that its integral along any straight line is [math]0[/math], be [math]0[/math] everywhere?
Let [math]f: \mathbb{R} \to \mathbb{R}[/math] be a real function. Can we prove or disprove: If [math]f[/math] is continuous and [math]f(\mathbb{R}) =\mathbb{R}[/math], then is [math]f[/math] monotone?