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KCET2018MathematicsContinuity and Differentiability

If [ f(x)= array cl 1+ kx - 1- kx x ; & if -1 x 0 2 x +1 x -1 ; & if 0 x 1 array . ] is continuous at ( x=0 ), then the value of ( k ) is

Options

  1. A( k=1 )
  2. B( k=-1 )
  3. C( k=0 )
  4. D( k=2 )

Correct answer

B. ( k=-1 )

Step-by-step solution

Given that [ f(x)= array cc 1+k x - 1-k x x & ;-1 x For continues at ( x=0 ), we have [ _ x 0⁻ f(x)= _ x 0⁺ f(x) ] [ array l So, _ x 0⁻ 1+k x - 1-k x x = _ x 0⁻ 2 k( 1-k x + 1+k x ) x( x ) =k and _ x 0⁺ 2 x+1 x-1 =-1=k So, k=-1 array ]

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