Fixed value theorem of continuous function Let f (x) be continuous on a closed interval [1,3] (1) If f (1) + F (2) + F (3) = 3, try to prove that there is at least one point a on [1,3] so that f (a) = 1

F(1）+F（2）+F(3)=3
It can be assumed that:
F(1)=1+a
F(2)=1+b
F(3)=1+c
a. B, C satisfy a + B + C = 0
A, B, C: 1
If a = b = C = 0, then:
F(1)=F(2)=F(3)=1
It can take any one of a = 1,2,3
a. If B and C are not all 0, then one of them must be greater than 0 and the other less than 0
Suppose a > 0, B1, f (2)

Fixed value theorem of continuous function Let f (x) be continuous on a closed interval [1,3] (1) If f (1) + F (2) + F (3) = 3, try to prove that there is at least one point a on [1,3] so that f (a) = 1

Fixed value theorem of continuous function Let f (x) be continuous on a closed interval [1,3] (1) If f (1) + F (2) + F (3) = 3, try to prove that there is at least one point a on [1,3] so that f (a) = 1

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