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NDA2015MathematicsContinuity and DifferentiabilityActual

Consider the function f(x)= array cc -2 x & if x - 2 A x+B & if - 2 x 2 x & if x 2 array . which is continuous everywhere. The value of A is

Options

  1. A1
  2. B0
  3. C-1
  4. D-2

Correct answer

C. -1

Step-by-step solution

f(x)= array ccc -2 x & if & x - / 2 A x+B & if & - / 2 x / 2 x & if & x / 2 array . aligned & f ( x ) is continuous every where: & _ x / 2 f ( x )= _ x / 2 f ( x ) & _ x / 2 x = _ x / 2 ~A x + B & ~A + B =0 aligned Also; _ x - / 2⁺ f(x)= _ x - / 2⁻ f(x) aligned & _ x - / 2 ~A x + B = _ x - / 2 -2 x & - A + B =2 aligned is from eq(1) & (2) we get, A=-1

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