The x-intercept of a graph (or function) is where the graph intercepts the x-axis.
The x-axis is given by the equation y=0, so the x-intercepts are the solutions to the simultaneous equations y=f(x) and y=0, or, x=f-1(0) and y=0 - also written (f-1(0), 0).
It is possible a function has no x-intercepts, it is possible it has one, it is possible it has many. For example, f(x) = x2 + 1 has no x-intercepts, f(x) = x2 has one x-intercept (at 0), f(x) = x2 - 1 has two intercepts (at -1 and 1), f(x) = x - ⌊x⌋ has an infinite number of x-intercepts (at each integer).