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KVPY2017MathematicsFunctions

Let f ( x )= (1+ x ² ) and A be a constant such that | f ( x )- f ( y )| | x - y | A for all x , y real and x y . Then the least possible value of A is

Options

  1. Aequal to 1
  2. Bbigger than 1 but less than 2
  3. Cbigger than 0 but less than 1
  4. Dbigger than 2

Correct answer

A. equal to 1

Step-by-step solution

f(x)= 2 x 1+x² Range of 2 x 1+x² [-1,1] |f(x)-f(y)| |x-y| A means maximum value of | f ( x )- f ( y )| | x - y | is always less than or equal to A . So, least value of A is 1

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