Let `f:[0,1] rarr [0,1]` be a continuous function. Then prove that `f(x)=x` for at least one `0lt=xlt=1.`

Let f:[0,1]rarr[0,1] be a continuous function. Then prove that f(x)=x for at least one 0<=x<=1

Let f:[0,1]to[0,1] be a continuous function. Then prove that f(x)=x for at least one 0lt=xlt=1.

Let f:[0,1]rarr[0,1] be a continuous function such that f(f(x))=1f or allx in[0,1] then

Let f : [0, 1] rarr [0, 1] be a continuous function such that f (f (x))=1 for all x in[0,1] then:

Let f:[0,1]to R be a continuous function then the maximum value of int_(0)^(1)f(x).x^(2)dx-int_(0)^(1)x.(f(x))^(2)dx for all such function(s) is:

Let f:[0,1]rarrR be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ?

Let f:[0,1]rarrR be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ?

Prove that f(x)=|1-x+|x|| is a continuous function at x=0