8. (2nd "Hope Cup" Senior High School Competition Question) The expression $[x]$ represents the greatest integer not exceeding the real number $x$, and the function $f(x) = x - [x]$ can be expressed in the form of a linear function. This form is $f(x)=$ $\qquad$ .
8. $f(x)=x-[x]$ has a graph roughly as shown in Figure 1-1. It can be solved using induction:
In the interval $[0,1)$, $f(x)=x$;
In the interval $[1,2)$, $f(x)=x-1$;
In the interval $[2,3)$, $f(x)=x-2$;
...
In the interval $[-1,0)$, $f(x)=x+1=x-(-1)$;
In the interval $[-2,-1)$, $f(x)=x+2=x-(-2)$; ...

Therefore, $f(x)=x-k, k \in \mathbf{Z}, x \in[k, k+1)$.