TE 0 1 SolutionLEt gxfxx If g00 or f10 then we have found th

Solution

LEt, g(x)=f(x)-x

If, g(0)=0 or f(1)=0 then we have found the x so that f(x)=x

Else,

g(0)=f(0)-0>0

g(1)=f(1)-1>0

Hence by Intermediate Value Theorem there is some c in (0,1) so that g(c)=0

Claim is not valid if f is not continous as Intermediate Value Theorem applies only to continous functions