Ms. Kang has explained, her explanation is not as clear as you d

I try to explain you another way, with your math language:

1) you know f(2) = 0, f(5)=8, f(8)=0

2) f(x) is continue function, so there is a A, 2<A<5, and f(A)=2; and a B, 5<B<8, f(B)=2

since 2 is between 0 and 8

3) you will get f(f(A))=f(f(B))=f(2) = 0, and f(f(5))=f(8)=0

so she said f(f(x)) would have 3 roots (no use to calculate A and B, as you did)

give you the same explanation,