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NEST2019MathematicsFunctions

Let f:[0,1] [0,1] be a non-constant continuous function different from the identity function. Then

Options

  1. Athe graph of f meets the line y=x at least once
  2. Bthere exists x₀ [0,1 / 2] such that f (x₀ )=f (x₀+1 / 2 ) if f(0)=f(1)
  3. Cthe set x [0,1]: f(f(x))=x is empty
  4. Dthere exists y₀ [0,1] such that ₀^ y₀ f(t) d t= _ y₀ ^1 f(t) d t

Correct answer

D. there exists y₀ [0,1] such that ₀^ y₀ f(t) d t= _ y₀ ^1 f(t) d t

Step-by-step solution

No solution available.

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