True or false, need help, thank you?

True of false: If f(x) is continuous and 0%26lt;=f(x)%26lt;=1 for all x in the interval [0,1], then for some number x, f(x)=x. Explain your answerTrue or false, need help, thank you?
yes it is true


as f(x) is%26lt;= 1


n function is continuous this means its graph doesnt break..


therefore there must exist a value for x at which f(x) = x





the value must be x =1


at which f(x) = x = 1 above


so the statemnt is true





draw a graph of this with thes points n u will see when x = 1 f(x) is also 1





poins x = 0 1


f(x) = 0 1


plot (0,0) %26amp; (1,1) on graph %26amp; restrict f(x) between 0 %26amp; 1





it will be a straight line...n it crosses origin...but u just see the aea between 0 %26amp; 1 ..GRAPH LOOKS LIKE THIS


NOW U CAN SEE WEN X = 1 f(x) =1 ...draw it on a paper











|____________________line f(x) = 1


1| /


| /


| /


| /____________________


0 1True or false, need help, thank you?
Do what you feel is right.