Solution to Continuous Function: Find x in [0,1] with f(x)=x

[jmich79]

Suppose that f is ais continuos function defined on [0,1] with f(0)=1 and f(1)=0. show that there is a value of x that in [0,1] such that f(x)=x.
I just do not understand this concept. Cna someone worjk this problem out for me and explain what's going on? Thank You.

 

[Office_Shredder]

You take a look at f(x)-x=g(x)

g(0)=1-0=1
g(1)=0-1=-1

So on [0,1] g is continuous and goes from 1 to -1. Hence, the intermediate value theorem gives you your answer. This is like, the third thread you've made on this, and if you can't get the answer from this post, you should probably go look up the intermediate value theorem and see what it actually says