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KCET2017MathematicsSets and Relations

If ( f(x)= aligned K x³ ; & if x 2 3 ; & if x>2 aligned . ) is continuous at ( x=2 ), then the value of ( K ) is

Options

  1. A( 13 )
  2. B( 04 )
  3. C3/4
  4. D( 4 / 3 )

Correct answer

C. 3/4

Step-by-step solution

Given that ( f(x)= array cc K ² & x 2 3 & x>2 array . ) Since, ( f(x) ) is continuous at ( x=2 ). Then, L.H.L = R.H.L So, ( _ x 2 K x²= _ x 2 3 ) ( K 2²=3 K= 3 4 )

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