Hello,

I am not sure how to address the following two continuity problems, they are quite similar to one another.

1) Suppose thatg(x)is a continuous function on [0,1] and that 0<=g(x)<=1 for allx∈ [0,1]. Show that there is a value ofxin [0, 1] whereg(x)= x.

2) Suppose thatg(x)is a continuous function on [0,2] withg(0) =g(2). Show that there is a value ofxin [0,1] such thatg(x)=g(x+1).

Thank you in advance for the help.