4. Given the functions $f(x)=2^{x}-1, g(x)=1-x^{2}$, the function $F(x)$ is defined as follows: when $|f(x)| \geqslant g(x)$, $F(x)=|f(x)|$; when $|f(x)|<g(x)$, $F(x)=$ $-g(x)$, then $F(x)($,$) .$
A. has a minimum value of 0, no maximum value
B. has a minimum value of -1, no maximum value
C. has a maximum value of 1, no minimum value
D. has neither a minimum value nor a maximum value
4. B. In the same coordinate system, draw the graphs of the functions $|f(x)|$ and $g(x)$, and solve by the graph.