第一题：假设连续。设 f(x) 是在x的时间从A到B，g(x) 从B到A。let h(x) = f(x) - g(x)

f(A)= 0, g(B) = 0

f(B) > 0, g(A) > 0

Therefore h(A) < 0 and h(B) > 0

by Intermediate value theorem, there exists a point C between A and B such that h(C) = 0.