KVPY SX SB Exam 2018 Question Paper

Question : 16 of 120

Marks: +1, -0

The number of functions f : [0, 1] → [0, 1] satisfying |f(x) – f(y)| = |x – y| for all x, y in [0, 1] is

Solution:

\lim ↙{x→y}|{ \f(x) -\f(y) }/{x-y}|=1

⇒ |f’(x)| = 1
f’(x) = ± 1
f (x) = x or f(x) = 1 – x (∵ f : [0, 1] → [0, 1])

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