Let S be the set of all twice differentiable functions f from to such that for all x…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let S be the set of all twice differentiable functions f from 
to such that 
for all x ∈(–1,1). For f ∈ S, let Xf be the number of points x ∈(–1, 1) for which
f(x) = x. Then which of the following statements is(are) true?
to such that for all x ∈(–1,1). For f ∈ S, let Xf be the number of points x ∈(–1, 1) for which f(x) = x. Then which of the following statements is(are) true?
- There exists a function f ∈ S such that Xf = 0
- For every function f ∈ S , we have Xf ≤ 2
- There exists a function f ∈S such that Xf = 2
- There does NOT exist any function f in S such that Xf = 1
Answer
(D) There does NOT exist any function f in S such that X f = 1
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